Amílcar Soares

geoENV VII: Geostatistics for Environmental Applications

We propose a hierarchical model coupled to geostatistics to deal with a non-gaussian data distribution and take explicitly into account complex spatial structures (i.e. trends, patchiness and random fluctuations). A common characteristic of animal count data is a distribution that is both zero-inflated and heavy tailed. In such cases, empirical variograms are no more robust and most structural analyses result in poor and noisy estimated spatial variogram structures. Thus kriged maps feature a broad variance of prediction. Moreover, due to the heterogeneity of wildlife population habitats, a nonstationary model is often required. To avoid these difficulties, we propose a hierarchical model that assumes that the count data follow a Poisson distribution given a theoretical sighting density which is a latent variable to be estimate. This density is modelled as the product of a positive long range trend by a positive stationary random field, characterized by a unit mean and a variogram function. A first estimate of the drift is used to obtain an estimate of the variogram of residuals including a correction term for variance coming from the Poisson distribution and weights due to the non-constant spatial mean. Then a kriging procedure similar to a modified universal kriging is implemented to directly map the latent density from raw count data. An application on fin whale data illustrates the effectiveness of the method in mapping animal density in a context that is presumably non-stationary. E. Bellier and P. Monestiez Biostatistique et Processus Spatiaux, INRA, Domaine Saint-Paul, Site Agroparc, 84914 Avignon cedex 9, France E. Bellier ( ) Norwegian Institute for Nature Research NINA, NO-7485 Trondheim, NORWAY e-mail: edwige.bellier@nina.no C. Guinet Centre d’Etudes Biologiques de Chize, CNRS, 79360 Villiers-en-Bois, France P.M. Atkinson and C.D. Lloyd (eds.), geoENV VII – Geostatistics for Environmental Applications, Quantitative Geology and Geostatistics 16, DOI 10.1007/978-90-481-2322-3 1, c Springer Science+Business Media B.V. 2010 1

Geostatistics Tróia '92

Theory petroleum other applications - environment, hydrology, soil sciences, natural resources, human sciences, mining.

Direct Sequential Simulation and Cosimulation

Sequential simulation of a continuous variable usually requires its transformation into a binary or a Gaussian variable, giving rise to the classical algorithms of sequential indicator simulation or sequential Gaussian simulation. Journel (1994) showed that the sequential simulation of a continuous variable, without any prior transformation, succeeded in reproducing the covariance model, provided that the simulated values are drawn from local distributions centered at the simple kriging estimates with a variance corresponding to the simple kriging estimation variance. Unfortunately, it does not reproduce the histogram of the original variable, which is one of the basic requirements of any simulation method. This has been the most serious limitation to the practical application of the direct simulation approach. In this paper, a new approach for the direct sequential simulation is proposed. The idea is to use the local sk estimates of the mean and variance, not to define the local cdf but to sample from the global cdf. Simulated values of original variable are drawn from intervals of the global cdf, which are calculated with the local estimates of the mean and variance. One of the main advantages of the direct sequential simulation method is that it allows joint simulation of Nv variables without any transformation. A set of examples of direct simulation and cosimulation are presented.

Improving the use of lichens as biomonitors of atmospheric metal pollution

The data reported on this study supported the hypothesis that the absence of the lichen Ramalina fastigiata near a copper mine site located on the south of Portugal was related to toxic levels of Cu-dust near the centre of the mine. Lichen biodiversity reflected the impact of the copper-mine dust emissions which were more widespread towards the east, correlated with wind direction and frequency. The chemical analysis of R. fastigiata collected at different distances and in different directions from the mine showed that Cu, K and Mg were derived from the centre of the mine site, confirming thus as the major source of atmospheric dust. Total inhibition of PSII photochemical reactions occurred in R. fastigiata both under field and controlled conditions, when intracellular Cu concentrations exceeded a threshold of approximately 2.0 mumol g-1. No samples of this species were found under field conditions beyond the Cu threshold. Thus, the fluorescence parameter Fv/Fm proved to be a good estimator of the survival capacity of R. fastigiata under field conditions and thus a useful parameter in determining the sensitivity of the lichens (photobiont) to Cu pollution. The intracellular location of Cu allowed an explanation of the physiological changes and the survival of the species in the surroundings of the copper-mine.

Spatial modeling of PAHs in lichens for fingerprinting of multisource atmospheric pollution.

PAHs are toxic compounds emitted by several anthropogenic sources, which have a great impact on human health. We show, for the first time, how spatial models based on PAHs intercepted by lichens can be used for fingerprinting multisource atmospheric pollution in a regional area. Urban-industrial areas showed the highest atmospheric deposition of PAHs followed by urban > industrial > agricultural > forest Multivariate analysis of lichen data showed, for the first time, a clear distinction between various sources of PAHs in the same area: urban are dominated by 4-ring PAHs, forest by 3-ring PAHs, and industrial by 5- and 6-ring PAHs or by 2-ring PAHs (petrogenic or pyrogenic, respectively). Heavy metals were also used for supporting the fingerprinting of PAH sources, reinforcing the industrial origin of 5- and 6-ring PAHs and revealing their particular nature. The spatial structure of the models for different PAHs seems to be dependent on the following factors: size and hydrophilic character of different PAHs, type of emission sources (point or nonpoint), and dispersion associated with particulates of different sizes. Based on the long-term integration of PAHs in lichens, these spatial models will significantly improve our knowledge on the impact of PAH chronic-exposure to humans and ecosystems.

Geostatistical estimation of multi-phase structures

A method is proposed for the characterization of the disjoint shapes of a multi-phase set. The method uses a global structural function and provides estimates of the complete mosaic of phases, honoring the individual volume proportions inferred from the experimental samples. The estimates of shapes can be improved by local conditioning to the covariance of each phase and to geometrical characteristics such as spatial orientation of the different strata. The mapping of uncertainty zones for individual phases is one advantage of using a geostatistical approach to characterize the morphology of qualitative (non-numerical) variables.

Assessing Human Exposure to Polycyclic Aromatic Hydrocarbons (PAH) in a Petrochemical Region Utilizing Data from Environmental Biomonitors

Polycyclic aromatic hydrocarbons (PAH) are toxic compounds that have been classified by the International Agency for Research on Cancer as probable or possible human carcinogens. Human exposure to PAH is usually assessed by considering data from a single air monitoring station as being representative of a large region; however, air pollution levels change on small spatial scales and thus also affect environmental exposure. The use of environmental biomonitors is a useful tool to assess the levels of PAH with high spatial resolution. The aims of this study were to (1) assess human exposure to PAH in a petrochemical region in Portugal, integrating data from environmental biomonitors (lichens), air, and soil in a regional area, and (2) determine the health risks associated with exposure to PAH with high spatial resolution. Bearing this in mind, benzo[a]pyrene (BaP) equivalent concentrations in samples of soil, air, and lichens collected in the study region were used to assess human exposure through different pathways, including inhalation of air and soil particles, ingestion of soil, and dermal contact with soil. Human health risk was calculated through the Incremental Lifetime Cancer Risk (ILCR). BaP equivalent concentrations found in the region ranged from 6.9 to 46.05 ng BaPeq/g in lichens, from 16.45 to 162.02 ng BaPeq/g in soils, and from 0.02 to 0.16 ng BaPeq/m3 in air, indicative of high variability in this regional area. Human exposure to PAH varied between 976 and 42,877 ng BaPeq/d. When considering all exposure pathways, ILCR values were between 10-4 and 10-3. Considering only inhalation, ILCR values were between 10-6 and 10-5. The main risk seemed to arise from soil (either ingestion or inhalation of resuspended soil particles). The high spatial resolution of our environmental data allowed for detection of critical exposure levels at unexpected sites. Our results identified important areas where health studies on local populations need to be focused, and where environmental levels of PAH need to be monitored over time in order to protect human health.

Geostatistical estimation of orebody geometry : morphological kriging

Most geostatistical approaches to the estimation of orebody geometry fail to make full use of the morphological information available and, as such, provide very simplistic and often unsatisfactory models of the shape and location of the orebody. The purpose of this paper is to describe a method of kriging an indicator variable subject to certain morphological information and then transforming the estimates into a binary map; the technique is termedmorphological kriging. Two case studies are used as examples to show that the method reproduces the morphological characteristics of the orebody, in so far as they can be conveyed by the information contained in the samples, while minimizing the smoothing effect of the estimator.

Stochastic Inversion with a Global Perturbation Method

Geostatistics has been commonly used in forward modeling and in inverse modeling to integrate seismic information in stochastic fine gride models. The quality of seismic and the downscaling of seismic attributes to the fine grid of the well measurements are still challenges to which existing geostatistical methods only give partial answers. In this paper an iterative inversion methodology is proposed based on a direct sequential simulation and co-simulation approaches. Several images of acoustic impedances of entire field are simulated in a first step. Afterwards, co-simulations are used for the global transformation of images of acoustic impedances in an iterative process: after the convolution, local areas of best fit of the different images are selected and “merged” into a secondary image for the direct co-simulation of the next iteration. The iterative and convergent process continues until a given match with an objective function is reached. Spatial dispersion and patterns of acoustic impedances (histograms and variograms) are reproduced at the final acoustic impedance cube.

Identification of Inhomogeneities in Precipitation Time Series Using Stochastic Simulation

Accurate quantification of observed precipitation variability is required for a number of purposes. However, high quality data seldom exist because in reality many types of non-climatic factors can cause time series discontinuities which may hide the true climatic signal and patterns, and thus potentially bias the conclusions of climate and hydrological studies. We propose the direct sequential simulation (DSS) approach for inhomogeneities detection in precipitation time series. Local probability density functions, calculated at known monitoring stations locations, by using spatial and temporal neighbourhood observations, are used for detection and classification of inhomogeneities. This stochastic approach was applied to four precipitation series using data from 62 surrounding stations located in the southern region of Portugal (1980–2001). Among other tests, three well established statistical tests were also applied: the Standard normal homogeneity test (SNHT) for a single break, the Buishand range test and the Pettit test. The inhomogeneities detection methodology is detailed, and the results from the testing procedures are compared and discussed.