Soil contamination from urban and industrial activity: example of the mining district of Linares (southern Spain)

The Linares region (southern Spain) has been subjected to two important sources of pollution: the intensive mining works and the urban-industrial activity. To obtain a geochemical characterisation of the soil, 31 trace elements were analysed and 669 soil samples were collected. By means of clustering analysis, we identified groups of elements and grid squares in which relations could be established concerning soil lithology, urban and industrial activities and the degree of pollution impact; in addition, we were able to characterise the geochemical background of the study area. The multivariate study led us to identify four factors. Particularly important was factor 2, which represented the elements associated with mineral paragenesis (Cu, Pb, As, Co, Mn, Zn, Sn, Ba). This factor also contains elements related with an urban-industrial activity, such as Pb, Cu, Zn, As and Ba. Furthermore, we identified factor 4, associating Ni, V and Cr, and which is related to the use of fuels.     

Soil erosion susceptibility assessment and validation using a geostatistical multivariate approach: a test in Southern Sicily

A certain number of studies have been carried out in recent years that aim at developing and applying a model capable of assessing water erosion of soil. Some of these have tried to quantitatively evaluate the volumes of soil loss, while others have focused their efforts on the recognition of the areas most prone to water erosion processes. This article presents the results of a research whose objective was that of evaluating water erosion susceptibility in a Sicilian watershed: the Naro river basin. A geomorphological study was carried out to recognize the water erosion landforms and define a set of parameters expressing both the intensity of hydraulic forces and the resistance of rocks/soils. The landforms were mapped and classified according to the dominant process in landsurfaces affected by diffuse or linear water erosion. A GIS layer was obtained by combining six determining factors (bedrock lithology, land use, soil texture, plan curvature, stream power index and slope-length factor) in unique conditions units. A geostatistical multivariate approach was applied by analysing the relationships between the spatial distributions of the erosion landforms and the unique condition units. Particularly, the density of eroded area for each combination of determining factors has been calculated: such function corresponds, in fact, to the conditional probability of erosion landforms to develop, under the same geoenvironmental conditions. In light of the obtained results, a general geomorphologic model for water erosion in the Naro river basin can be depicted: cultivated areas in clayey slopes, having fine-medium soil texture, are the most prone to be eroded; linear or diffuse water erosion processes dominate where the topography is favourable to a convergent or divergent runoff, respectively. For each of the two erosion process types, a susceptibility map was produced and submitted to a validation procedure based on a spatial random partition strategy. Both the success of the validation procedure of the susceptibility models and the geomorphological coherence of the relationships between factors and process that such models suggest, confirm the reliability of the method and the goodness of the predictions.     

Optimizing interpolation of shoot density data from a Posidonia oceanica seagrass bed

A case study on the optimization of Posidonia oceanica density interpolation, using a data set from a large meadow at Porto Conte Bay (NW Sardinia, Italy), is presented. Ordinary point kriging, cokriging and a weighted average based on inverse square distance were used to interpolate density data measured in 36 sampling stations. The results obtained from different methods were then compared by means of a leave‐one‐out cross‐validation procedure. The scale at which interpolation was carried out was defined on the basis of the Hausdorff dimension of the variogram. Optimizing spatial scale and data points search strategy allowed obtaining more accurate density estimates independently of the interpolation method.     

On the geologic structure of the Explora Escarpment (Weddell Sea,Antarctica) revealed by satellite and Shipboard data evaluation

Bathymetric, gravity, and magnetic data from Antarctic expeditions with RV POLARSTERN and satellite altimeter data from the Geosat Geodetic Mission are analysed using methods from geostatistics and geophysical inverse theory.The Explora Escarpment represents the edge between the Antarctic Continental Shelf and the Weddell Abyssal Plain. It is an important link in the reconstruction of Gondwana breakup, but a feature as large as the 2000 m deep Wegener Canyon was only discovered in 1984, when extensive bathymetric, gravimetric, and magnetic surveys with RV POLARSTERN began.Geostatistics, the theory of regionalized variables, is applied to integrate dense surveys of Wegener Canyon and sparse observations in adjacent areas into maps with full coverage of the 230 km by 330 km area at 10°–20° W/70°–72° S. The resultant highresolution bathymetric and gravity maps reveal detailed structures of the Explora Escarpment. Using geophysical inversion, the gravity terrain effect is calculated. Satellite data are used for their better coverage, but have much lower resolution. Nevertheless, the structures of Wegener Canyon and other more prominent features appear with surprisingly good correlation also in the Geosat altimeter data. While it was initially supposed that Wegener Canyon is purely an erosional structure, the magnetic map now provides evidence of the canyon's tectonic origin.     

Heavy metals in marine sediments of Taranto Gulf (Ionian Sea, Southern Italy)

Al, Cr, Cu, Fe, Hg, Mn, Ni, Pb, Ti and Zn concentrations have been determined in surface sediment samples collected in the Taranto Gulf (Ionian Sea, Southern Italy) in order to evaluate their levels and spatial distribution in this important area of the Mediterranean Sea. For various metals, the geoaccumulation index has been calculated as a criterion to assess if their concentrations represent contamination levels or can be considered as background levels. The results show that metals concentrations in sediments can be considered near the background levels found in the Mediterranean Sea.Analytical results have been elaborated by using a Geographical Information System (GIS) software to show metals accumulation areas. Using multivariate statistical analysis, we evaluate the possibility to distinguish the sampling stations, in relation to their geographical position. Results have showed metals distribution in the Taranto Gulf is principally influenced by industrial and urban wastes, located mostly in the northern coastal area of the Ionian Sea. Rivers in the Basilicata region and prevailing anticlockwise marine currents are further factors influencing metal accumulation in sediments.     

Prediction of UT1–UTC,LOD and AAM χ<Subscript>3</Subscript> by combination of least-squares and multivariate stochastic methods

This article presents the application of a multivariate prediction technique for predicting universal time (UT1–UTC), length of day (LOD) and the axial component of atmospheric angular momentum (AAM χ ₃). The multivariate predictions of LOD and UT1–UTC are generated by means of the combination of (1) least-squares (LS) extrapolation of models for annual, semiannual, 18.6-year, 9.3-year oscillations and for the linear trend, and (2) multivariate autoregressive (MAR) stochastic prediction of LS residuals (LS + MAR). The MAR technique enables the use of the AAM χ ₃ time-series as the explanatory variable for the computation of LOD or UT1–UTC predictions. In order to evaluate the performance of this approach, two other prediction schemes are also applied: (1) LS extrapolation, (2) combination of LS extrapolation and univariate autoregressive (AR) prediction of LS residuals (LS + AR). The multivariate predictions of AAM χ ₃ data, however, are computed as a combination of the extrapolation of the LS model for annual and semiannual oscillations and the LS + MAR. The AAM χ ₃ predictions are also compared with LS extrapolation and LS + AR prediction. It is shown that the predictions of LOD and UT1–UTC based on LS + MAR taking into account the axial component of AAM are more accurate than the predictions of LOD and UT1–UTC based on LS extrapolation or on LS + AR. In particular, the UT1–UTC predictions based on LS + MAR during El Niño/La Niña events exhibit considerably smaller prediction errors than those calculated by means of LS or LS + AR. The AAM χ ₃ time-series is predicted using LS + MAR with higher accuracy than applying LS extrapolation itself in the case of medium-term predictions (up to 100 days in the future). However, the predictions of AAM χ ₃ reveal the best accuracy for LS + AR.     

On the multivariate total least-squares approach to empirical coordinate transformations. Three algorithms

The multivariate total least-squares (MTLS) approach aims at estimating a matrix of parameters, Ξ, from a linear model (Y−E _Y = (X−E _X ) · Ξ) that includes an observation matrix, Y, another observation matrix, X, and matrices of randomly distributed errors, E _Y and E _X . Two special cases of the MTLS approach include the standard multivariate least-squares approach where only the observation matrix, Y, is perturbed by random errors and, on the other hand, the data least-squares approach where only the coefficient matrix X is affected by random errors. In a previous contribution, the authors derived an iterative algorithm to solve the MTLS problem by using the nonlinear Euler–Lagrange conditions. In this contribution, new lemmas are developed to analyze the iterative algorithm, modify it, and compare it with a new ‘closed form’ solution that is based on the singular-value decomposition. For an application, the total least-squares approach is used to estimate the affine transformation parameters that convert cadastral data from the old to the new Israeli datum. Technical aspects of this approach, such as scaling the data and fixing the columns in the coefficient matrix are investigated. This case study illuminates the issue of “symmetry” in the treatment of two sets of coordinates for identical point fields, a topic that had already been emphasized by Teunissen (1989, Festschrift to Torben Krarup, Geodetic Institute Bull no. 58, Copenhagen, Denmark, pp 335–342). The differences between the standard least-squares and the TLS approach are analyzed in terms of the estimated variance component and a first-order approximation of the dispersion matrix of the estimated parameters.     

Modelling Positional Uncertainty of Line Features by Accounting for Stochastic Deviations from Straight Line Segments

The assessment of positional uncertainty in line and area features is often based on uncertainty in the coordinates of their elementary vertices which are assumed to be connected by straight lines. Such an approach disregards uncertainty caused by sampling and approximation of a curvilinear feature by a sequence of straight line segments. In this article, a method is proposed that also allows for the latter type of uncertainty by modelling random rectangular deviations from the conventional straight line segments. Using the model on a dense network of sub‐vertices, the contribution of uncertainty due to approximation is emphasised; the sampling effect can be assessed by applying it on a small set of randomly inserted sub‐vertices. A case study demonstrates a feasible way of parameterisation based on assumptions of joint normal distributions for positional errors of the vertices and the rectangular deviations and a uniform distribution of missed sub‐vertices along line segments. Depending on the magnitudes of the different sources of uncertainty, not accounting for potential deviations from straight line segments may drastically underestimate the positional uncertainty of line features.     

Hierarchical decomposition of variance with applications in environmental mapping based on satellite images

A quadtree-based image segmentation procedure (HQ) is presented to map complex environmental conditions. It applies a hierarchical nested analysis of variance within the framework of multiresolution wavelet approximation. The procedure leads to an optimal solution for determining mapping units based on spatial variability with constraints on the arrangement and shape of the units. Linkages to geostatisiics are pointed out, but the HQ decomposition algorithm does not require any homogeneity criteria. The computer implementation can be parameterized by either the number of required mapping units or the maximum within-unit variance, or it can provide a spectrum of significances of nested ANOVA. The detailed mathematical background and methodology is illustrated by a salt-affected grassland mapping study (Hortobágy, Hungary), where heterogeneous environmental characteristics have been sampled and predicted based on remotely sensed images using these principles.     

Efficient generation of conditional simulations by chebyshev matrix polynomial approximations to the symmetric square root of the covariance matrix

Consider the problem of generating a realization y₁ of a Gaussian random field on a dense grid of points ₁ conditioned on field observations y₂ collected on a sparse grid of points ₂. An approach to this is to generate first an unconditional realization y over the grid =_{1 2}, and then to produce y₁ by conditioning y on the data y₂. As standard methods for generating y, such as the turning bands, spectral or Cholesky approaches can have various limitations, it has been proposed by M. W. Davis to generate realizations from a matrix polynomial approximations to the square root of the covariance matrix. In this paper we describe how to generate a direct approximation to the conditional realization y₁, on ₁ using a variant of Davis' approach based on approximation by Chebyshev polynomials. The resulting algorithm is simple to implement, numerically stable, and bounds on the approximation error are readily available. Furthermore we show that the conditional realization y₁ can be generated directly with a lower order polynomial than the unconditional realization y, and that further reductions can be achieved by exploiting a nugget effect if one is present. A pseudocode version of the algorithm is provided that can be implemented using the fast Fourier transform if the field is stationary and the grid ₁ is rectangular. Finally, numerical illustrations are given of the algorithm's performance in generating various 2-D realizations of conditional processes on large sampling grids.