An iterative optimization scheme to accommodate inequality constraints in air quality geostatistical estimation of multivariate PM

The kriging-based estimation of the different types of atmospheric particulate matter (PM) pollutions defined in the air quality regulation raises some operational problems because the (co)kriging equations are obtained by minimizing a linear combination of the estimation variances subject to unbiasedness constraints. As a consequence, the estimation process can result in total PM₁₀ concentrations that are less than the PM_2.5 concentrations which would be physically impossible. In a previous publication, it was shown that a convenient external drift modeling can reduce the number of spatial locations where the inequality constraint is not satisfied, without completely solving the problem. In this work, the formulation of the cokriging system is modified, inspired by previous works focusing on positive kriging. The introduction of additional constraints on the cokriging weights are presented, leading to a unique and optimal solution to the problem of cokriging under inequality constraints between two variables. Some computational and algorithmic details are introduced. An evaluation of the penalized cokriging is provided by using the European PM monitoring sites dataset: some maps and performance scores are given to assess the relevance of our iterative optimization scheme.

Nail Samples of Children Living near Coal Ash Storage Facilities Suggest Fly Ash Exposure and Elevated Concentrations of Metal(loid)s

Children who live near coal-fired power plants are exposed to coal fly ash, which is stored in landfills and surface impoundments near residential communities. Fly ash has the potential to be released as fugitive dust. Using data collected from 263 children living within 10 miles of coal ash storage facilities in Jefferson and Bullitt Counties, Kentucky, USA, we quantified the elements found in nail samples. Furthermore, using principal component analysis (PCA), we investigated whether metal(loid)s that are predominately found in fly ash loaded together to indicate potential exposure to fly ash. Concentrations of several neurotoxic metal(loid)s, such as chromium, manganese, and zinc, were higher than concentrations reported in other studies of both healthy and environmentally exposed children. From PCA, it was determined that iron, aluminum, and silicon in fly ash were found to load together in the nails of children living near coal ash storage facilities. These metal(loid)s were also highly correlated with each other. Last, results of geospatial analyses partially validated our hypothesis that children's proximity to power plants was associated with elevated levels of concentrations of fly ash metal(loid)s in nails. Taken together, nail samples may be a powerful tool in detecting exposure to fly ash.

Data-Driven Intelligent 3D Surface Measurement in Smart Manufacturing: Review and Outlook

High-fidelity characterization and effective monitoring of spatial and spatiotemporal processes are crucial for high-performance quality control of many manufacturing processes and systems in the era of smart manufacturing. Although the recent development in measurement technologies has made it possible to acquire high-resolution three-dimensional (3D) surface measurement data, it is generally expensive and time-consuming to use such technologies in real-world production settings. Data-driven approaches that stem from statistics and machine learning can potentially enable intelligent, cost-effective surface measurement and thus allow manufacturers to use high-resolution surface data for better decision-making without introducing substantial production cost induced by data acquisition. Among these methods, spatial and spatiotemporal interpolation techniques can draw inferences about unmeasured locations on a surface using the measurement of other locations, thus decreasing the measurement cost and time. However, interpolation methods are very sensitive to the availability of measurement data, and their performances largely depend on the measurement scheme or the sampling design, i.e., how to allocate measurement efforts. As such, sampling design is considered to be another important field that enables intelligent surface measurement. This paper reviews and summarizes the state-of-the-art research in interpolation and sampling design for surface measurement in varied manufacturing applications. Research gaps and future research directions are also identified and can serve as a fundamental guideline to industrial practitioners and researchers for future studies in these areas.

Spatial interpolation methods to predict airborne pesticide drift deposits on soils using knapsack sprayers

Spatial predictions of drift deposits on soil surface were conducted using eight different spatial interpolation methods i.e. classical approaches like the Thiessen method and kriging, and some advanced methods like spatial vine copulas, Karhunen-Loève expansion and INLA. In order to investigate the impact of the number of locations on the prediction, all spatial predictions were conducted using a set of 39 and 47 locations respectively. The analysis revealed that taking more locations into account increases the accuracy of the prediction and the extreme behavior of the data is better modeled. Leave-one-out cross-validation was used to assess the accuracy of the prediction. The Thiessen method has the highest prediction errors among all tested methods. Linear interpolation methods were able to better reproduce the extreme behavior at the first meters from the sprayed border and exhibited lower prediction errors as the number of data points increased. Especially the spatial copula method exhibited an obvious increase in prediction accuracy. The Karhunen-Loève expansion provided similar results as universal kriging and IDW, although showing a stronger change in the prediction as the number of locations increased. INLA predicted the pesticide dispersion to be smooth over the whole study area. Using Delaunay triangulation of the study area, the total pesticide concentration was estimated to be between 2.06% and 2.97% of the total Uranine applied. This work is a first attempt to completely understand and model the uncertainties of the mass balance, therefore providing a basis for future studies.

Exploring spatiotemporal patterns of PM2.5 in China based on ground-level observations for 190 cities

Whereas air pollution in many Chinese cities has reached epidemic levels in recent years, limited research has explored the spatial and temporal patterns of fine air particles such as PM2.5, or particulate matter with diameter smaller than 2.5 μm, using nationally representative data. This article applied spatial statistical approaches including spatial interpolation and spatial regression to the analysis of ground-level PM2.5 observations for 190 Chinese cities in 2014 obtained from the Chinese Air Quality Online Monitoring Platform. Results of this article suggest that most Chinese cities included in the dataset recorded severe levels of PM2.5 in excess of the WHO's interim target and cities in the North China Plain had the highest levels of PM2.5 regardless of city size. Spatially interpolated maps of PM2.5 and population-weighted PM2.5 indicate vast majority of China's land and population was exposed to disastrous levels of PM2.5 concentrations. The regression results suggest that PM2.5 in a city was positively related to its population size, amount of atmospheric pollutants, and emissions from nearby cities, but inversely related to precipitation and wind speed. Findings from this research can shed new light on the complex spatiotemporal patterns of PM2.5 throughout China and provide insights into policies aiming to mitigate air pollution in China.

Identifiability for non-stationary spatial structure

For modelling non-stationary spatial random fields Z = {Z(x) : x∊ℝn, n≥2} a recent method has been proposed to deform bijectively the index space so that the spatial dispersion D(x,y) = var[Z(x)-Z(y)], (x,y)∊ℝnxℝn, depends only on the Euclidean distance in the deformed space through an isotropic variogram γ. We prove uniqueness of this model in two different cases: (i) γ is strictly increasing; (ii) γ(u) is differentiable for u > 0.

Identifiability for non-stationary spatial structure

For modelling non-stationary spatial random fields Z = {Z(x) : x∊ℝ n , n≥2} a recent method has been proposed to deform bijectively the index space so that the spatial dispersion D(x,y) = var[Z(x)-Z(y)], (x,y)∊ℝ n xℝ n , depends only on the Euclidean distance in the deformed space through an isotropic variogram γ. We prove uniqueness of this model in two different cases: (i) γ is strictly increasing; (ii) γ(u) is differentiable for u > 0.

Nonstationary patterns of isolation-by-distance: inferring measures of local genetic differentiation with Bayesian kriging

Patterns of isolation-by-distance (IBD) arise when population differentiation increases with increasing geographic distances. Patterns of IBD are usually caused by local spatial dispersal, which explains why differences of allele frequencies between populations accumulate with distance. However, spatial variations of demographic parameters such as migration rate or population density can generate nonstationary patterns of IBD where the rate at which genetic differentiation accumulates varies across space. To characterize nonstationary patterns of IBD, we infer local genetic differentiation based on Bayesian kriging. Local genetic differentiation for a sampled population is defined as the average genetic differentiation between the sampled population and fictive neighboring populations. To avoid defining populations in advance, the method can also be applied at the scale of individuals making it relevant for landscape genetics. Inference of local genetic differentiation relies on a matrix of pairwise similarity or dissimilarity between populations or individuals such as matrices of F_ST between pairs of populations. Simulation studies show that maps of local genetic differentiation can reveal barriers to gene flow but also other patterns such as continuous variations of gene flow across habitat. The potential of the method is illustrated with two datasets: single nucleotide polymorphisms from human Swedish populations and dominant markers for alpine plant species.

A bivariate space-time downscaler under space and time misalignment

Ozone and particulate matter PM(2.5) are co-pollutants that have long been associated with increased public health risks. Information on concentration levels for both pollutants come from two sources: monitoring sites and output from complex numerical models that produce concentration surfaces over large spatial regions. In this paper, we offer a fully-model based approach for fusing these two sources of information for the pair of co-pollutants which is computationally feasible over large spatial regions and long periods of time. Due to the association between concentration levels of the two environmental contaminants, it is expected that information regarding one will help to improve prediction of the other. Misalignment is an obvious issue since the monitoring networks for the two contaminants only partly intersect and because the collection rate for PM(2.5) is typically less frequent than that for ozone.Extending previous work in Berrocal et al. (2009), we introduce a bivariate downscaler that provides a flexible class of bivariate space-time assimilation models. We discuss computational issues for model fitting and analyze a dataset for ozone and PM(2.5) for the ozone season during year 2002. We show a modest improvement in predictive performance, not surprising in a setting where we can anticipate only a small gain.

A conditional expectation approach for associating ambient air pollutant exposures with health outcomes

Our research focuses on the association between exposure to an airborne pollutant and counts of emergency department visits attributed to a specific chronic illness. The motivating example for this analysis of measurement error in time series studies of air pollution and acute health outcomes was a study of emergency department visits from a 20-county Atlanta metropolitan statistical area from 1993-1999. The research presented illustrates the impact of using various surrogates for unobserved measurements of ambient concentrations at the zip code level. Simulation results indicate that the impact of measurement error on the association between pollutant exposure and a health outcome can be substantial. The proposed conditional expectation approach provided reliable estimates of the association and exhibited good confidence interval coverage for a variety of magnitudes of association. Use of a single-centrally located monitor, the arithmetic average, the nearest-neighbor monitor, and the inverse-distance weighted average surrogates resulted in biased estimates and poor coverage rates, especially for larger magnitudes of the association. A focus on obtaining reasonable exposure measurements within clearly defined subregions is important when the pollutant exposure of interest exhibits strong spatial variability.

Modeling mercury deposition through latent space-time processes

This paper provides a space-time process model for total wet mercury deposition. Key methodological features introduced include direct modeling of deposition rather than of expected deposition, the utilization of precipitation information (there is no deposition without precipitation) without having to construct a precipitation model, and the handling of point masses at 0 in the distributions of both precipitation and deposition. The result is a specification that enables spatial interpolation and temporal prediction of deposition as well as aggregation in space or time to see patterns and trends in deposition.We use weekly deposition monitoring data from the NADP/MDN (National Atmospheric Deposition Program/Mercury Deposition Network) for 2003 restricted to the eastern U.S. and Canada. Our spatio-temporal hierarchical model allows us to interpolate to arbitrary locations and, hence, to an arbitrary grid, enabling weekly deposition surfaces (with associated uncertainties) for this region. It also allows us to aggregate weekly depositions at coarser, quarterly and annual, temporal levels.

High Resolution Space-Time Ozone Modeling for Assessing Trends

The assessment of air pollution regulatory programs designed to improve ground level ozone concentrations is a topic of considerable interest to environmental managers. To aid this assessment, it is necessary to model the space-time behavior of ozone for predicting summaries of ozone across spatial domains of interest and for the detection of long-term trends at monitoring sites. These trends, adjusted for the effects of meteorological variables, are needed for determining the effectiveness of pollution control programs in terms of their magnitude and uncertainties across space. This paper proposes a space-time model for daily 8-hour maximum ozone levels to provide input to regulatory activities: detection, evaluation, and analysis of spatial patterns of ozone summaries and temporal trends. The model is applied to analyzing data from the state of Ohio which has been chosen because it contains a mix of urban, suburban, and rural ozone monitoring sites in several large cities separated by large rural areas. The proposed space-time model is auto-regressive and incorporates the most important meteorological variables observed at a collection of ozone monitoring sites as well as at several weather stations where ozone levels have not been observed. This problem of misalignment of ozone and meteorological data is overcome by spatial modeling of the latter. In so doing we adopt an approach based on the successive daily increments in meteorological variables. With regard to modeling, the increment (or change-in-meteorology) process proves more attractive than working directly with the meteorology process, without sacrificing any desired inference. The full model is specified within a Bayesian framework and is fitted using MCMC techniques. Hence, full inference with regard to model unknowns is available as well as for predictions in time and space, evaluation of annual summaries and assessment of trends.

Using GIS-Based Approaches to Support Research on Neurotoxicants and Other Children's Environmental Health Threats

Environmental threats to children's health are complex and multifaceted; consequently, children's environmental health research strives to identify areas of elevated exposure, determine whether particular demographic groups are inequitably exposed, and link exposures to incidence of disease. Many environmental health researchers use geographic information systems (GIS) to ex post display the results of their data collection and analysis. This methodological paper shows some ways by which the ex ante integration of GIS into environmental exposure and epidemiological research can significantly enhance: research design; sampling, recruitment, and retention strategies; data management and analysis; and community translation.

Comparison of spatial interpolation methods for the estimation of air quality data

We recognized that many health outcomes are associated with air pollution, but in this project launched by the US EPA, the intent was to assess the role of exposure to ambient air pollutants as risk factors only for respiratory effects in children. The NHANES-III database is a valuable resource for assessing children's respiratory health and certain risk factors, but lacks monitoring data to estimate subjects' exposures to ambient air pollutants. Since the 1970s, EPA has regularly monitored levels of several ambient air pollutants across the country and these data may be used to estimate NHANES subject's exposure to ambient air pollutants. The first stage of the project eventually evolved into assessing different estimation methods before adopting the estimates to evaluate respiratory health. Specifically, this paper describes an effort using EPA's AIRS monitoring data to estimate ozone and PM10 levels at census block groups. We limited those block groups to counties visited by NHANES-III to make the project more manageable and apply four different interpolation methods to the monitoring data to derive air concentration levels. Then we examine method-specific differences in concentration levels and determine conditions under which different methods produce significantly different concentration values. We find that different interpolation methods do not produce dramatically different estimations in most parts of the US where monitor density was relatively low. However, in areas where monitor density was relatively high (i.e., California), we find substantial differences in exposure estimates across the interpolation methods. Our results offer some insights into terms of using the EPA monitoring data for the chosen spatial interpolation methods.

Testing for common structures in a panel of threshold models

We consider the problem of examining the extent of (partial) similarity in the dynamics of a panel of independent threshold autoregressive processes. We develop some tests for common structure via Wald's approach and by checking whether the parameter estimates of the unconstrained threshold models satisfy the constraints defining the common structure. One test concerns the equality of independent ratios of normal means, which is shown to have nonstandard asymptotic null distribution. These tests are illustrated with a modern panel of Canadian lynx data; our analysis suggests that the lynx data over Canada share similar dynamics in the decrease phase, but they appear to be different in the increase phase.

Estimating long-term average particulate air pollution concentrations: application of traffic indicators and geographic information systems

BACKGROUND

As part of a multicenter study relating traffic-related air pollution with incidence of asthma in three birth cohort studies (TRAPCA), we used a measurement and modelling procedure to estimate long-term average exposure to traffic-related particulate air pollution in communities throughout the Netherlands; in Munich, Germany; and in Stockholm County, Sweden.

METHODS

In each of the three locations, 40-42 measurement sites were selected to represent rural, urban background and urban traffic locations. At each site and fine particles and filter absorbance (a marker for diesel exhaust particles) were measured for four 2-week periods distributed over approximately 1-year periods between February 1999 and July 2000. We used these measurements to calculate annual average concentrations after adjustment for temporal variation. Traffic-related variables (eg, population density and traffic intensity) were collected using Geographic Information Systems and used in regression models predicting annual average concentrations. From these models we estimated ambient air concentrations at the home addresses of the cohort members.

RESULTS

Regression models using traffic-related variables explained 73%, 56% and 50% of the variability in annual average fine particle concentrations for the Netherlands, Munich and Stockholm County, respectively. For filter absorbance, the regression models explained 81%, 67% and 66% of the variability in the annual average concentrations. Cross-validation to estimate the model prediction errors indicated root mean squared errors of 1.1-1.6 microg/m for PM(2.5) and 0.22-0.31 *10(-5) m for absorbance.

CONCLUSIONS

A substantial fraction of the variability in annual average concentrations for all locations was explained by traffic-related variables. This approach can be used to estimate individual exposures for epidemiologic studies and offers advantages over alternative techniques relying on surrogate variables or traditional approaches that utilize ambient monitoring data alone.

A critical examination of ozone mapping from a spatial-scale perspective

Following the establishment of point measurements of ground-level ozone concentrations have been attempts by many researchers to develop ozone surfaces. This paper offers a critique of ozone-mapping endeavors, while also empirically exploring the operational scale of ground-level ozone. The following issues are discussed: aspects of spatial scale; the spatial complexity of ground-level ozone concentrations; and the problems of previous attempts at ozone mapping. Most ozone-mapping studies are beset with at least one of the following core problems: spatial-scale violations; an improper evaluation of surfaces; inaccurate surfaces; and the inappropriate use of surfaces in certain analyses. The major recommendations to researchers are to acknowledge spatial scale (especially operational scale), understand the prerequisites of surface-generating techniques, and to evaluate the resultant ozone surface properly.

Long-term air pollution indicator assessment: example of black smoke in Bordeaux, France

The aim of the second phase of the Pollution Atmosphérique et Affections Respiratoires Chroniques (PAARC) study, started in 1974, was to compare the long-term mortality between populations living in areas with different air pollution levels. In Bordeaux (France), four different areas were concerned by the study. The black smoke measures were realized between 1974 and 1981. After 1981, the stations set specifically for the study were not used any more. The purpose of this study was to estimate the evolution of air pollution in those areas between 1982 and 1997 using the measures of 12 Association de Prévention de la Pollution Atmosphérique (APPA) stations located in Bordeaux city but not in the PAARC areas. The method used was divided in three phases: a correlation study between the stations of the different networks, a selection of the pertinent stations and the setting up of indicators using the arithmetic means method. Monthly means concentrations were estimated from January 1982 to December 1997. Models showed a decrease in black smoke levels whatever the area. The difference in level from one area to another, existing between the areas in 1974, was still with predicted values in 1997, but less important. Black smoke mean concentration for 1982-1997 was, respectively, 16.4 and 16.2 microg/m3, in areas 1 and 2. It was a little bit higher in area 3 with 18.9 microg/m3. Area 4 still has the highest level with 26.3 microg/m3. To conclude, this method enabled to assess different air pollution levels at different times in the four areas of the PAARC study in Bordeaux. Those levels could be used to study the impact of the air pollution on long-term mortality on populations living in the areas considered.