Multivariate Spatial Outlier Detection Using Robust Geographically Weighted Methods

Outlier detection is often a key task in a statistical analysis and helps guard against poor decision-making based on results that have been influenced by anomalous observations. For multivariate data sets, large Mahalanobis distances in raw data space or large Mahalanobis distances in principal components analysis, transformed data space, are routinely used to detect outliers. Detection in principal components analysis space can also utilise goodness of fit distances. For spatial applications, however, these global forms can only detect outliers in a non-spatial manner. This can result in false positive detections, such as when an observation’s spatial neighbours are similar, or false negative detections such as when its spatial neighbours are dissimilar. To avoid mis-classifications, we demonstrate that a local adaptation of various global methods can be used to detect multivariate spatial outliers. In particular, we account for local spatial effects via the use of geographically weighted data with either Mahalanobis distances or principal components analysis. Detection performance is assessed using simulated data as well as freshwater chemistry data collected over all of Great Britain. Results clearly show value in both geographically weighted methods to outlier detection.     

Relationships between rocky desertification and spatial pattern of land use in typical karst area,Southwest China

Karst rocky desertification is a typical type of land degradation in the Southwest China. An attempt was made to study quantitatively the relationships between rocky desertification and spatial pattern of land use through applying spatial analysis of Geographical Information System in Nandong underground river system, a typical karst area, Southwest China. The spatial distribution of rocky desertification and spatial pattern of land use were obtained from interpreting Landsat Images in Nandong area in 2007 by supervised classifications, and verified and rectified through field survey. The results indicate that: (1) the total land deserted area covers 378.3 km², or 23.4% of the total area, of which intense, moderate and slight rocky desertification covers 269.46, 54.2, and 54.63 km², respectively, in Nandong area. (2) There is an obvious effect of spatial pattern of land use on rocky desertification. With the increase of elevation and slope, there is a higher occurrence ratio of rocky desertification in the cultivated land and grass land. Also, more than half of total rocky desertification was dominated within the areas of 4 km from the construction land, and 97% of total rocky desertification was dominated within the areas of 10 km from the construction land in Nandong area. And what can be known from the data is that the primary effect distance of human on rocky desertification from the construction land is 4 km, and the farthest effect distance of human on rocky desertification from the construction land is 10 km in Nandong area.     

Divergent behaviour of Th and U during anatexis: Implications for the thermal evolution of orogenic crust

Mobilization and migration of the heat‐producing elements (HPE) during anatexis is a critical process in the development of orogenic systems, the evolution of continental crust and the stabilization of cratons. In many crustal rocks the accessory minerals are the dominant hosts of Th and U, and the behaviour of these minerals during partial melting controls the concentrations of these elements in draining melt and residue. We use phase equilibrium modelling to evaluate if loss of melt saturated in the essential structural constituents of the accessory minerals can explain the concentrations of Th and U in residual metasedimentary migmatites and granulites along two well‐characterized crustal transects in the Ivrea zone, Italy and at Mt Stafford, Australia. While an equilibrium model of accessory mineral breakdown and melt loss approximates the depletion of U in the residual crust along both transects, it does not explain the relative enrichment of Th. We propose that the high Th concentrations in residual crust may be explained by either inhibition of monazite dissolution by kinetic factors or near‐peak growth of new high Th grains and overgrowth rims on undissolved monazite due to migration of melt through the orogenic crust. Retention of the HPE in the middle and deep orogenic crust may allow metasedimentary granulites to overcome the enthalpy barrier of melting to achieve ultrahigh temperature conditions and may be partly responsible for the slow cooling of many granulite terranes. Lastly, although the mantle was warmer and crustal heat production was higher in the past, peak temperatures and apparent thermal gradients of high‐temperature (HT)–ultrahigh temperature (UHT) granulite terranes have not decreased significantly since the Neoarchean. However, the pressure of HP granulite facies metamorphism has increased gradually from the Archean to the Phanerozoic, which suggests that the lithosphere became stronger as secular cooling of the mantle enabled plate collisions to form thicker orogens. Thus, as the lithosphere became stronger, the proportion of HT–UHT metamorphism associated with thin lithosphere and mantle heat has decreased, whereas the proportion associated with the formation of thick crust and radiogenic heat has increased.     

Landscape influences on aluminium and dissolved organic carbon in streams draining the Hubbard Brook valley,New Hampshire,USA

Concentrations of both aluminium (Al) and dissolved organic carbon (DOC) in stream waters are likely to be regulated by factors that influence water flowpaths and residence times, and by the nature of the soil horizons through which waters flow. In order to investigate landscape‐scale spatial patterns in streamwater Al and DOC, we sampled seven streams draining the Hubbard Brook valley in central New Hampshire. We observed considerable variation in stream chemistry both within and between headwater watersheds. Across the valley, concentrations of total monomeric aluminium (Al_m) ranged from below detection limits (<0·7 µmol l⁻¹) to 22·3 µmol l⁻¹. In general, concentrations of Al_m decreased as pH increased downslope. There was a strong relationship between organic monomeric aluminium (Al_o) and DOC concentrations (R² = 0·92). We observed the highest Al_m concentrations in: (i) a watershed characterized by a steep narrow drainage basin and shallow soils and (ii) a watershed characterized by exceptionally deep forest floor soils and high concentrations of DOC. Forest floor depth and drainage area together explained much of the variation in ln Al_m (R² = 0·79; N = 45) and ln DOC (R² = 0·87; N = 45). Linear regression models were moderately successful in predicting ln Al_m and ln DOC in streams that were not included in model building. However, when back‐transformed, predicted DOC concentrations were as much as 72% adrift from observed DOC concentrations and Al_m concentrations were up to 51% off. This geographic approach to modelling Al and DOC is useful for general prediction, but for more detailed predictions, process‐level biogeochemical models are required. Copyright © 2005 John Wiley & Sons, Ltd.