Search

Abstract: The estimation of geographical attributes is a crucial matter for many real-world problems, and the issue of accuracy stands out when the estimation is used for between-regions comparison. In this work, our concern is area attribute estimation in a GIS environment. We estimate the area attribute value with a mean Kriging technique, and the probability distribution of the estimate is derived. This is the best linear unbiased observed spatial population mean estimate and can be used in more relaxed situations than the block Kriging technique. Both theoretical analysis and empirical study show that the mean Kriging technique outperforms the ordinary Kriging, spatial random sampling, and simple random sampling techniques in estimating the observable spatial population mean across space.

Since the COVID-19 outbreak, four cities—Wuhan, Beijing, Urumqi and Dalian—have experienced the process from outbreak to stabilization. According to the China Statistical Yearbook and China Center for Disease Control records, regional, pathological, medical and response attributes were selected as regional vulnerability factors of infectious diseases. Then the Analytic Hierarchy Process (AHP) method was used to build a regional vulnerability index model for the infectious disease. The influence of the COVID-19 outbreak at a certain place was assessed computationally in terms of the number of days of epidemic duration and cumulative number of infections, and then fitted to the city data. The resulting correlation coefficient was 0.999952. The range of the regional vulnerability index for COVID-19 virus was from 0.0513 to 0.9379. The vulnerability indexes of Wuhan, Urumqi, Beijing and Dalian were 0.8733, 0.1951, 0.1566 and 0.1119, respectively. The lack of understanding of the virus became the biggest breakthrough point for the rapid spread of the virus in Wuhan. Due to inadequate prevention and control measures, the city of Urumqi was unable to trace the source of infection and close contacts, resulting in a relatively large impact. Beijing has both high population density and migration rate, which imply that the disease outbreak in this city had a great impact. Dalian has perfect prevention and good regional attributes. In addition, the regional vulnerability index model was used to analyze other Chinese cities. Accordingly, the regional vulnerability index and the prevention and control suggestions for them were discussed.

Accurate risk assessment of heavy metal pollution in soil is a prerequisite for environmental and human health protection. Due to the spatial heterogeneity in the environment, biased results can be obtained when uniform background values are introduced in regional heavy metal pollution assessment. In this study, considering the heavy metal background variation in different regions, 209 surface samples and 18 deep samples were collected from soils developed from different parent materials. In addition, the pollution level, environmental, and health risks and spatial pattern were analyzed. The results indicated that the overall mean concentrations of Cr, Pb, As, Cd, and Hg were 60.02, 39.79, 14.32, 0.38, and 0.18 mg/kg, respectively. Moreover, heavy metals exhibited significantly different pollution levels and environmental risks among soils developed from the different parent materials: due to the higher accumulation and toxicity response coefficients for Cd, Hg, and As, heavy metal pollution and ecological risks in soils developed from plain river alluvium and granite eluvium were higher than those in soils developed from the other parent materials. Regarding human health risks, ingestion was found to be the main exposure pathway, and children exhibited higher noncarcinogenic and carcinogenic risks than the adults. Heavy metal pollution in soils developed from granite eluvium indicated a significantly higher health risk than those in soils developed from the other parent materials due to higher As accumulation. The assessment index spatial distributions revealed that high-risk areas mainly occurred in the eastern broad valley plain, central river valley plain, and northwestern mountain areas, demonstrating that due to intensive human activities, heavy metal accumulation in these areas yielded higher risks. When formulating soil pollution prevention measures, attention should be directed toward high-risk areas to achieve sustainable environmental development.

Human activities interacting with coastal waters lead to large amounts of nutrient loading and severe water pollution in China's near Seas. In this context, a comprehensive quantitative characterization of the spatiotemporal variation of nutrient pollutant concentrations is a key component of any reliable seawater quality assessment and integrated coastal management plan. The present work combines the Bayesian maximum entropy method with stochastic site indicators to estimate monthly nitrate and phosphate concentrations in China's near seas during 2015, explore their spatiotemporal variation, and provide an explicit quantitative assessment of seawater quality in conditions of in situ uncertainty. This makes it the first study of space‐time nutrient pollutant characterization at a national‐scale in a coastal seawater environment. The results showed that nitrate and phosphate distributions exhibit the same spatial trends along China's near seas, whereas high nutrient pollution levels are found in the Yangtze River, Liaohe River, and Pearl River estuaries. Local differences of temporal trends exist between nitrate and phosphate distributions, which suggest that distinct remediation strategies are needed to properly satisfy the required seawater quality standards. The average nitrate and phosphate concentrations across space‐time were found to be equal to 0.271 and 0.015 mg/L, respectively. The nitrate and phosphate concentrations exceeding the fourth grade seawater quality standard during 2015 were about 11% and 2.6%, respectively. The study of both the seasonal changes in human activities along the coastal cities and the temporal marine hydrodynamics can offer a better understanding of the seawater quality and the biogeochemical process of nutrient transport and distribution. Bayesian maximum entropy maps showed that nitrate and phosphate concentrations had similar spatial distributionsNitrate and phosphate distributions exhibited different seasonal patterns that may have been affected by coastal hydrodynamics and human activitiesStochastic site indicators showed that nitrate pollution was much more serious than phosphate pollution

Soil Cd and Zn were strongly correlated and characterized by generally similar spatial distribution.Agricultural soils on the Pembina Escarpment and Red River Valley had naturally high total and DTPA‐extractable Cd and Zn.Many soils of the Pembina Escarpment and Red River Valley had naturally high organic C and CEC.Parent materials of high clay content were derived from shale‐enriched glacial till or colluvium, alluvium, and lacustrine deposits.Distribution of Cd and Zn followed the distribution of parent materials and soil CEC, organic carbon, and texture. Cadmium and zinc are trace elements with many geochemical similarities, but Cd is non‐essential and potentially toxic to humans and animals, whereas Zn is an essential micronutrient. Understanding the distribution and availability of these elements in soils is necessary for managing their availability to plants and the accumulation of Cd in edible crops, such as durum wheat. We studied the distribution of Cd and Zn in agricultural soils across the 18 counties of northern North Dakota because this region produces the majority of durum wheat grown in the United States, and many varieties of durum tend to accumulate undesirable levels of Cd in grain. Surface and subsurface soils were sampled and analyzed for concentrations of total and DTPA‐extractable Cd and Zn, pH, organic carbon (OC), and cation exchange capacity (CEC). Soil parent materials were classified based on information in the Soil Survey Geographic database for North Dakota. The spatial dependencies of the concentrations of Cd and Zn, and their (Cd/Zn) were investigated by modeling spatial variograms, and the results used for kriging or co‐kriging to prepare maps of the distribution of these characteristics across northern North Dakota. The distribution of Cd and Zn in these glaciated soils of northern North Dakota appears to be determined largely by the distribution of soil parent materials and by the soil properties CEC, OC, and soil texture. Relatively high levels of Cd and Zn were found in soils derived naturally from clayey shale‐enriched till, colluvium, and lacustrine deposits near the Pembina Escarpment or in the Red River Valley.

Abstract: The estimation of geographical attributes is a crucial matter for many real-world problems, and the issue of accuracy stands out when the estimation is used for between-regions comparison. In this work, our concern is area attribute estimation in a GIS environment. We estimate the area attribute value with a mean Kriging technique, and the probability distribution of the estimate is derived. This is the best linear unbiased observed spatial population mean estimate and can be used in more relaxed situations than the block Kriging technique. Both theoretical analysis and empirical study show that the mean Kriging technique outperforms the ordinary Kriging, spatial random sampling, and simple random sampling techniques in estimating the observable spatial population mean across space.

A meaningful characterization of epidemiologic fields (mortality, incidence rate, etc.) often involves the assessment of their spatiotemporal variation at multiple scales. An adequate analysis should depend on the scale at which the epidemiologic field is considered rather than being limited by the scale at which the data are available. In many studies, for example, data are available at a larger scale (say, counties), whereas the epidemiologist is interested in a smaller-scale analysis (say, residential neighborhoods). We propose a mathematically rigorous and epidemiologically meaningful multiscale approach that uses the well-known BME theory to study important scale effects and generate informative scale-dependent maps. The approach is applied to a real-world case study involving daily mortality counts in the state of California. The approach accounts for scale effects and produces mortality predictions at the zip-code scale by downscaling data from the county scale. The multiscale approach is tested by means of a verification data set with detailed mortality information at the zip-code level for 1 day. A measure of mapping accuracy is used to demonstrate that the multiscale approach offers more accurate mortality predictions at the local scale than existing approaches, which do not account for scale effects.Journal of Exposure Analysis and Environmental Epidemiology (2003) 13, 120–133. doi:10.1038/sj.jea.7500263

The goal of this work is to discuss a general methodology for studying associations between environmental exposures and health effect by means of the spatiotemporal random field theory. This theory is the tool of choice for rigorously accounting for important spatiotemporal variations and uncertainties related to exposures and effect. Within the framework of the random field theory, the Bayesian maximum entropy model neatly synthesizes various sources of physical and epidemiological knowledge into spatiotemporal analysis. Therefore, unlike technical statistics, this approach relies on the blending of substantive physical knowledge with powerful mathematical techniques and a coherent rationale. Given the well-founded fact that certain health effects may be caused by environmental exposures, the significance of these exposures is assessed in terms of a criterion that is based on the joint stochastic representation of exposure and health-effect distributions in space/time. In view of this criterion, the strength and consistency of the exposure–effect association are evaluated on the basis of the health-effect predictions that the combined physico-epidemiologic analysis generates in space/time. The main features of the approach are demonstrated by a simulation example and a real case study involving mortality and cold temperatures in North Carolina. The studies demonstrated the practical usefulness of the stochastic human exposure analysis in assessing the exposure–effect association. The results reported here emphasize the links between spatiotemporal models of physical systems and population health-effect distributions, thus suggesting directions for improving the current understanding of quantitative “exposure–health effect” functions.Journal of Exposure Analysis and Environmental Epidemiology (2000) 10, 168–187. 10.1038/sj.jea.7500077

Exposure analysis and mapping of spatiotemporal pollutants in relation to their health effects are important challenges facing environmental health scientists and integrated assessment modellers. In this work, a methodological framework is discussed to study the impact of spatiotemporal ozone (O3) exposure distributions on the health of human populations. The framework, however, is very general and can be used to study various other pollutants. The spatiotemporal analysis starts with exposure distributions producing the input to pollutokinetic (or toxicokinetic) laws which are linked to effect models which, in turn, are integrated with relationships that describe how effects are distributed across populations. Important characteristics of the environmental health framework are holisticity and stochasticity. Holisticity emphasizes the functional relationships between composite space/time O3maps, pollutokinetic models of burden on target organs and tissues, and health effects. These relationships offer a meaningful physical interpretation of the exposure and biological processes that affect human exposure. Stochasticity involves the rigorous representation of natural uncertainties and biological variations in terms of spatiotemporal random fields. The stochastic perspective introduces a deeper epistemological understanding in the development of improved models of spatiotemporal human exposure analysis and mapping. Also, it explicitly determines the knowledge bases available and develops logically plausible rules and standards for data processing and human exposure map construction. The proposed approach allows the horizontal integration among sciences related to the human exposure problem that leads to accurate and informative spatiotemporal maps of O3exposure and effect distributions and an integrative analysis of the whole risk case. By processing a variety of knowledge bases, the spatiotemporal analysis can bring together several sciences which are all relevant to the aspect of human exposure reality that is examined.Journal of Exposure Analysis and Environmental Epidemiology (1999) 9, 322–335. 10.1038/sj.jea.7500033

A fundamental problem facing the physical sciences today is analysis of natural variations and mapping of spatiotemporal processes. Detailed maps describing the space/time distribution of groundwater contaminants, atmospheric pollutant deposition processes, rainfall intensity variables, external intermittency functions, etc. are tools whose importance in practical applications cannot be overestimated. Such maps are valuable inputs for numerous applications including, for example, solute transport, storm modeling, turbulent-nonturbulent flow characterization, weather prediction, and human exposure to hazardous substances. The approach considered here uses the spatiotemporal random field theory to study natural space/time variations and derive dynamic stochastic estimates of physical variables. The random field model is constructed in a space/time continuum that explicitly involves both spatial and temporal aspects and provides a rigorous representation of spatiotemporal variabilities and uncertainties. This has considerable advantages as regards analytical investigations of natural processes. The model is used to study natural space/time variations of springwater calcium ion data from the Dyle River catchment area, Belgium. This dataset is characterized by a spatially nonhomogeneous and temporally nonstationary variability that is quantified by random field parameters, such as orders of space/time continuity and random field increments. A rich class of covariance models is determined from the properties of the random field increments. The analysis leads to maps of continuity orders and covariances reflecting space/time calcium ion correlations and trends. Calcium ion estimates and the associated statistical errors are calculated at unmeasured locations/instants over the Dyle region using a space/time kriging algorithm. In practice, the interpretation of the results of the dynamic stochastic analysis should take into consideration the scale effects.

Abstract: This work presents a stochastic diagrammatic theory for the calculation of the effective hydraulic conductivity of heterogeneous media. The theory is based on the mean-flux series expansion of a log-normal hydraulic conductivity medium in terms of diagrammatic representations and leads to certain general results for the effective hydraulic conductivity of three-dimensional media. A selective summation technique is used to improve low-order perturbation analysis by evaluating an infinite set of diagrammatic terms with a specific topological structure that dominates the perturbation series. For stochastically isotropic media the selective summation yeilds the anticipated exponential expression for the effective hydraulic conductivity. This expression is extended to stochastically anisotropic media. It is also shown that in the case of non homogeneous media the uniform effective hydraulic conductivity is replaced by a non-local tensor kernel, for which general diagrammatic expressions are obtained. The non-local kernel leads to the standard exponential behavior for the effective hydraulic conductivity at the homogeneous limit.

Recursive algorithms for estimating states of nonlinear physical systems are presented. Orthogonality properties are rediscovered and the associated polynomials are used to linearize state and observation models of the underlying random processes. This requires some key hypotheses regarding the structure of these processes, which may then take account of a wide range of applications. The latter include streamflow forecasting, flood estimation, environmental protection, earthquake engineering, and mine planning. The proposed estimation algorithm may be compared favorably to Taylor series-type filters, nonlinear filters which approximate the probability density by Edgeworth or Gram-Charlier series, as well as to conventional statistical linearization-type estimators. Moreover, the method has several advantages over nonrecursive estimators like disjunctive kriging. To link theory with practice, some numerical results for a simulated system are presented, in which responses from the proposed and extended Kalman algorithms are compared.

In this study, developments in the theory of stochastic simulation are discussed. The unifying element is the notion of Radon projection in Euclidean spaces. This notion provides a natural way of reconstructing the real process from a corresponding process observable on a reduced dimensionality space, where analysis is theoretically easier and computationally tractable. Within this framework, the concept of space transformation is defined and several of its properties, which are of significant importance within the context of spatially correlated processes, are explored. The turning bands operator is shown to follow from this. This strengthens considerably the theoretical background of the geostatistical method of simulation, and some new results are obtained in both the space and frequency domains. The inverse problem is solved generally and the applicability of the method is extended to anisotropic as well as integrated processes. Some ill-posed problems of the inverse operator are discussed. Effects of the measurement error and impulses at origin are examined. Important features of the simulated process as described by geomechanical laws, the morphology of the deposit, etc., may be incorporated in the analysis. The simulation may become a model-dependent procedure and this, in turn, may provide numerical solutions to spatial-temporal geologic models. Because the spatial simulation may be technically reduced to unidimensional simulations, various techniques of generating one-dimensional realizations are reviewed. To link theory and practice, an example is computed in detail.

Parameter estimation has become increasingly interesting the last few decades for a variety of engineering topics. In such situations, one may face problems like (a) how to estimate parameters for which erroneous measurements are available (direct estimation), or (b) how to estimate coefficients of some process model governing a geological phenomenon when these coefficients are inaccessible or difficult to access by direct investigation (inverse estimation or identification). Both these problems are examined in this presentation from a modern stochastic viewpoint, where parameters sought are interpretated mathematically as random functions, generated and estimated in space or time with the aid of recursive models. Advantages of this methodology are remarkable, from both theoretical and physical points of view, as compared to conventional statistics or nonrecursive estimators. Particularly it may offer more accurate estimators, better representation of spatial variation, and a means of overcoming difficulties such as excessive computational time or computer storage. To test effectiveness of this type of estimation, a series of representative case studies from geotechnical practice have been computed in detail.

The purpose of this paper is to stress the importance of a Bayesian/maximum-entropy view toward the spatial estimation problem. According to this view, the estimation equations emerge through a process that balances two requirements: High prior information about the spatial variability and high posterior probability about the estimated map. The first requirement uses a variety of sources of prior information and involves the maximization of an entropy function. The second requirement leads to the maximization of a so-called Bayes function. Certain fundamental results and attractive features of the proposed approach in the context of the random field theory are discussed, and a systematic spatial estimation scheme is presented. The latter satisfies a variety of useful properties beyond those implied by the traditional stochastic estimation methods.

We formulate stochastic indicator parameters that characterize pollution levels in geographical regions with heterogeneous contaminant distributions. The indicator parameters are expressed in terms of the random fields representing the contaminant distributions and the critical threshold level specified by health and environmental standards. Certain theoretical results are proven regarding univariate and bivariate indicator parameters. The analytical expressions obtained are general and can be used in practice for various types of contaminant distributions. A test of ergodicity-breaking is suggested for scientific and engineering applications in terms of the indicator parameters. Fractal characteristics of the indicator parameters are discussed. The effects of modelling and observation scale on exceedance contamination analysis are examined. Indicator random field parameters are studied on both continuum and lattice domains using analytical means and numerical simulations.