George Christakos

Multiphase flow and transport modeling in heterogeneous porous media: challenges and approaches

Abstract We review the current status of modeling multiphase systems, including balance equation formulation, constitutive relations for both pressure-saturation-conductivity and interphase mass transfer, and stochastic and computational issues. We discuss weaknesses and inconsistencies of current approaches based on theoretical, computational, and experimental evidence. Where possible, we suggest new or evolving approaches.

A Bayesian/maximum-entropy view to the spatial estimation problem

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.

Geographical Detectors-Based Health Risk Assessment and its Application in the Neural Tube Defects Study of the Heshun Region, China

Physical environment, man‐made pollution, nutrition and their mutual interactions can be major causes of human diseases. These disease determinants have distinct spatial distributions across geographical units, so that their adequate study involves the investigation of the associated geographical strata. We propose four geographical detectors based on spatial variation analysis of the geographical strata to assess the environmental risks of health: the risk detector indicates where the risk areas are; the factor detector identifies factors that are responsible for the risk; the ecological detector discloses relative importance between the factors; and the interaction detector reveals whether the risk factors interact or lead to disease independently. In a real‐world study, the primary physical environment (watershed, lithozone and soil) was found to strongly control the neural tube defects (NTD) occurrences in the Heshun region (China). Basic nutrition (food) was found to be more important than man‐made pollution (chemical fertilizer) in the control of the spatial NTD pattern. Ancient materials released from geological faults and subsequently spread along slopes dramatically increase the NTD risk. These findings constitute valuable input to disease intervention strategies in the region of interest.

Bayesian Maximum Entropy Analysis and Mapping: A Farewell to Kriging Estimators?

The Bayesian Maximum Entropy (BME) method of spatial analysis and mapping provides definite rules for incorporating prior information, hard and soft data into the mapping process. It has certain unique features that make it a loyal guardian of plausible reasoning under conditions of uncertainty. BME is a general approach that does not make any assumptions regarding the linearity of the estimator, the normality of the underlying probability laws, or the homogeneity of the spatial distribution. By capitalizing on various sources of information and data, BME introduces an epistemological framework that produces predictive maps that are more accurate and in many cases computationally more efficient than those derived by traditional techniques. In fact, kriging techniques can be derived as special cases of the BME approach, under restrictive assumptions regarding the prior information and the data available. BME is a more rigorous approach than indicator kriging for incorporating soft data. The BME formulation, in fact, applies in a spatial or a spatiotemporal domain and its extension to the case of block and vector random fields is straightforward. New theoretical results are presented and numerical examples are discussed, which use the BME approach to account for important sources of knowledge in a systematic manner. BME can be useful in practical situations in which prior information can be used to compensate for the limited amount of measurements available (e.g., preliminary or feasibility study levels) or soft data are available that can be combined with hard data to improve mapping significantly. BME may be then viewed as an effort towards the development of a more general framework of spatial/temporal analysis and mapping, which includes traditional geostatistics as its limiting case, and it also provides the means to derive novel results that could not be obtained by traditional geostatistics.

Spatial analysis and mapping of sexually transmitted diseases to optimise intervention and prevention strategies

Objective: We analysed and mapped the distribution of four reportable sexually transmitted diseases, chlamydial infection/non-gonococcal urethritis (chlamydial infection), gonorrhoea, primary and secondary syphilis (syphilis), and HIV infection, for Wake County, North Carolina, to optimise an intervention. Methods: We used STD surveillance data reported to Wake County, for the year 2000 to analyse and map STD rates. STD rates were mathematically represented as a spatial random field. We analysed spatial variability by calculating and modelling covariance functions of random field theory. Covariances are useful in assessing spatial patterns of disease locally and at a distance. We combined observed STD rates and appropriate covariance models using a geostatistical method called kriging, to predict STD rates and associated prediction errors for a grid covering Wake County. Final disease estimates were interpolated using a spline with tension and mapped to generate a continuous surface of infection. Results: Lower incidence STDs exhibited larger spatial variability and smaller neighbourhoods of influence than higher incidence STDs. Each reported STD had a clustered spatial distribution with one primary core area of infection. Core areas overlapped for all four STDs. Conclusions: Spatial heterogeneity within STD suggests that STD specific prevention strategies should not be targeted uniformly across Wake County, but rather to core areas. Overlap of core areas among STDs suggests that intervention and prevention strategies can be combined to target multiple STDs effectively. Geostatistical techniques are objective, population level approaches to spatial analysis and mapping that can be used to visualise disease patterns and identify emerging outbreaks.

Spatiotemporal environmental health modelling : a tractatus stochasticus

I. Fundamental Principles of Stochastic Environmental Health Modelling. II. Environmental Exposure Fields and their Health Effects. III. Spatiotemporal Random Fields in Exposure Analysis and Assessment. IV. Modelling Exposure Heterogeneities. V. Spatiotemporal Mapping of Environmental Health Processes - the BME Approach. VI. Spatiotemporal MMSE Mapping. VII. Stochastic Partial Differential Equation Modelling of Flow and Transport. VIII. Stochastic Physiologically-Based Pollutokinetic Modelling. IX. Stochastic Exposure and Health Indicators. Bibliography. Index.

Hand, foot and mouth disease: spatiotemporal transmission and climate

BackgroundThe Hand-Foot-Mouth Disease (HFMD) is the most common infectious disease in China, its total incidence being around 500,000 ~1,000,000 cases per year. The composite space-time disease variation is the result of underlining attribute mechanisms that could provide clues about the physiologic and demographic determinants of disease transmission and also guide the appropriate allocation of medical resources to control the disease.Methods and FindingsHFMD cases were aggregated into 1456 counties and during a period of 11 months. Suspected climate attributes to HFMD were recorded monthly at 674 stations throughout the country and subsequently interpolated within 1456 × 11 cells across space-time (same as the number of HFMD cases) using the Bayesian Maximum Entropy (BME) method while taking into consideration the relevant uncertainty sources. The dimensionalities of the two datasets together with the integrated dataset combining the two previous ones are very high when the topologies of the space-time relationships between cells are taken into account. Using a self-organizing map (SOM) algorithm the dataset dimensionality was effectively reduced into 2 dimensions, while the spatiotemporal attribute structure was maintained. 16 types of spatiotemporal HFMD transmission were identified, and 3-4 high spatial incidence clusters of the HFMD types were found throughout China, which are basically within the scope of the monthly climate (precipitation) types.ConclusionsHFMD propagates in a composite space-time domain rather than showing a purely spatial and purely temporal variation. There is a clear relationship between HFMD occurrence and climate. HFMD cases are geographically clustered and closely linked to the monthly precipitation types of the region. The occurrence of the former depends on the later.

BME analysis of spatiotemporal particulate matter distributions in North Carolina

Abstract Spatiotemporal maps of particulate matter (PM) concentrations contribute considerably to the understanding of the underlying natural processes and the adequate assessment of the PM health effects. These maps should be derived using an approach that combines rigorous mathematical formulation with sound science. To achieve such a task, the PM10 distribution in the state of North Carolina is studied using the Bayesian maximum entropy (BME) mapping method. This method is based on a realistic representation of the spatiotemporal domain, which can integrate rigorously and efficiently various forms of physical knowledge and sources of uncertainty. BME offers a complete characterization of PM10 concentration patterns in terms of multi-point probability distributions and allows considerable flexibility regarding the choice of the appropriate concentration estimates. The PM10 maps show significant variability both spatially and temporally, a finding that may be associated with geographical characteristics, climatic changes, seasonal patterns, and random fluctuations. The inherently spatiotemporal nature of PM10 variation is demonstrated by means of theoretical considerations as well as in terms of the more accurate PM10 predictions of composite space/time analysis compared to spatial estimation. It is shown that the study of PM10 distributions in North Carolina can be improved by properly incorporating uncertain data into the mapping process, whereas more informative estimates are generated by considering soft data at the estimation points. Uncertainty maps illustrate the significance of stochastic PM10 characterization in space/time, and identify limitations associated with inadequate interpolation techniques. Stochastic PM10 analysis has important applications in the optimization of monitoring networks in space and time, environmental risk assessment, health management and administration, etc.

Estimation of citywide air pollution in Beijing.

There has been discrepancies between the daily air quality reports of the Beijing municipal government, observations recorded at the U.S. Embassy in Beijing, and Beijing residents’ perceptions of air quality. This study estimates Beijing’s daily area PM2.5 mass concentration by means of a novel technique SPA (Single Point Areal Estimation) that uses data from the single PM2.5 observation station of the U.S Embassy and the 18 PM10 observation stations of the Beijing Municipal Environmental Protection Bureau. The proposed technique accounts for empirical relationships between different types of observations, and generates best linear unbiased pollution estimates (in a statistical sense). The technique extends the daily PM2.5 mass concentrations obtained at a single station (U.S. Embassy) to a citywide scale using physical relations between pollutant concentrations at the embassy PM2.5 monitoring station and at the 18 official PM10 stations that are evenly distributed across the city. Insight about the technique’s spatial estimation accuracy (uncertainty) is gained by means of theoretical considerations and numerical validations involving real data. The technique was used to study citywide PM2.5 pollution during the 423-day period of interest (May 10, 2010 to December 6, 2011). Finally, a freely downloadable software library is provided that performs all relevant calculations of pollution estimation.

Modeling Spatial Means of Surfaces With Stratified Nonhomogeneity

In geosciences, one often needs to estimate the spatial means of surfaces representing physical attributes. Under certain conditions, this kind of estimation is often performed by a simple summation of a random sample or by some kind of a Kriging (spatial regression) technique. For example, the naive sample mean assumes that the sample is randomly distributed across space, which is a restrictive assumption with limited applicability in real-world situations (e.g., in the case of nonhomogeneous surfaces, the naive sample mean is a biased estimate of the actual surface mean). Kriging techniques can generate unbiased estimates for certain kinds of homogeneous surfaces but may be not appropriate in cases of stratified nonhomogeneity when the covariances exhibit considerable differences between different strata of the surface. In this paper, we extend the Kriging concept to study surfaces with stratified nonhomogeneity. The corresponding analytical formulas are derived, and empirical studies are performed that involve real-world and simulated data sets. Numerical comparative analysis showed that the proposed method performed well compared to other methods commonly used for the purpose of estimating surface means across space.