Estimation of covariance matrix from geochemical data with observations below detection limits

Multivariate statistical analyses have been extensively applied to geochemical measurements to analyze and aid interpretation of the data. Estimation of the covariance matrix of multivariate observations is the first task in multivariate analysis. However, geochemical data for the rare elements, especially Ag, Au, and platinum-group elements, usually contain observations the below detection limits. In particular, Instrumental Neutron Activation Analysis (INAA) for the rare elements produces multilevel and possibly extremely high detection limits depending on the sample weight. Traditionally, in applying multivariate analysis to such incomplete data, the observations below detection limits are first substituted, for example, each observation below the detection limit is replaced by a certain percentage of that limit, and then the standard statistical computer packages or techniques are used to obtain the analysis of the data. If a number of samples with observations below detection limits is small, or the detection limits are relatively near zero, the results may be reasonable and most geological interpretations or conclusions are probably valid. In this paper, a new method is proposed to estimate the covariance matrix from a dataset containing observations below multilevel detection limits by using the marginal maximum likelihood estimation (MMLE) method. For each pair of variables, sayY andZ whose observations containing below detection limits, the proposed method consists of three steps: (i) for each variable separately obtaining the marginal MLE for the means and the variances, , , , and forY andZ: (ii) defining new variables by and and lettingA=C+D andB=C–D, and obtaining MLE for variances, and forA andB; (iii) estimating the correlation coefficient _YZ by and the covariance _YZ by . The procedure is illustrated by using a precious metal geochemical data set from the Fox River Sill, Manitoba, Canada.     

Mapping landslide susceptibility from small datasets: A case study in the Pays de Herve (E Belgium)

A landslide susceptibility map is proposed for the Pays de Herve (E Belgium), where large landslides affect Cretaceous clay outcrop areas. Based on a Bayesian approach, this GIS-supported probabilistic map identifies the areas most susceptible to deep landslides. The database is comprised of the source areas of ten pre-existing landslides (i.e. a sample of 154 grid cells) and of six environmental data layers, namely lithology, proximity to active faults, slope angle and aspect, elevation and distance to the nearest valley-floor. A 30-m-resolution DEM from the Belgian National Geographical Institute is used for the analysis. Owing to the small size of the sample, a special cross-validation procedure of the susceptibility map is performed, which uses in an iterative way each of the landslides to test the predictive power of the map derived from the other landslides. Four different sets of variables are used to produce four susceptibility maps, whose prediction curves are compared. While the prediction rates associated with the models not involving the “proximity to active fault” criterion are comparable to those of the models considering this variable, strong weaknesses inherent in the fault data on which the latter rely suggest that the final susceptibility map should be based on a model that excludes any reference to fault. This highlights the difference between a triggering factor and determining factors, and in the same time broadens the scope of the produced map. A single reactivated slide is also used to test the possibility of predicting future reactivation of existing landslides in the area. Finally, the need for geomorphological control over the mathematical treatment is underlined in order to obtain realistic prediction maps.     

Application of integrated back‐propagation network and self organizing map for flood forecasting

Much of the nonlinearity and uncertainty regarding the flood process is because hydrologic data required for estimation are often tremendously difficult to obtain. This study employed a back‐propagation network (BPN) as the main structure in flood forecasting to learn and to demonstrate the sophisticated nonlinear mapping relationship. However, a deterministic BPN model implies high uncertainty and poor consistency for verification work even when the learning performance is satisfactory for flood forecasting. Therefore, a novel procedure was proposed in this investigation which integrates linear transfer function (LTF) and self‐organizing map (SOM) to efficiently determine the intervals of weights and biases of a flood forecasting neural network to avoid the above problems. A SOM network with classification ability was applied to the solutions and parameters of the BPN model in the learning stage, to classify the network parameter rules and to obtain the winning parameters. The outcomes from the previous stage were then used as the ranges of the parameters in the recall stage. Finally, a case study was carried out in Wu‐Shi basin to demonstrate the effectiveness of the proposal. Copyright © 2009 John Wiley & Sons, Ltd.     

Evaluating the stress intensity factors of anisotropic bimaterials using boundary element method

This paper presents a boundary element method (BEM) procedure for a linear elastic fracture mechanics analysis in two‐dimensional anisotropic bimaterials. In this formulation, a displacement integral equation is only collocated on the uncracked boundary, and a traction integral equation is only collocated on one side of the crack surface. A fundamental solution (Green's function) for anisotropic bimaterials is also derived and implemented into the boundary integral formulation so that except for the interfacial crack part, the discretization along the interface can be avoided. A special crack‐tip element is introduced to capture the exact crack‐tip behavior. A computer program using FORTRAN has been developed to effectively calculate the stress intensity factors of an anisotropic bimaterial. This BEM program has been verified to have a good accuracy with previous studies. In addition, a central cracked bimaterial Brazilian specimen constituting cement and gypsum is prepared to conduct the Brazilian test under diametral loading. The result shows that the numerical analysis can predict relatively well the direction of crack initiation and the path of crack propagation. Copyright © 2007 John Wiley & Sons, Ltd.     

Grain size trend and hydrodynamic condition of tirumalairajan River estuary,east coast of India

The estuary can be considered as environments characterized by high productivity and uncommensurable ecological value. However, marine ecosystems are also subjected to high human pressures that increase their vulnerability. The aim of this work is to analyze grain size trend of sediment due to the action of the main hydrodynamic condition. The spatial distribution patterns of sediments were monitored according to season. The grain-size trend of surficial sediments revealed a dominant sediment transport trend towards the eastern and south eastern part of study area. This study shows that there is an agreement among sediments path ways, hydrodynamic condition and the sediment spatial distribution in the estuarine environment. The agitation by waves is an important sorting mechanism in the study area. The findings are based on the grain size trend and also corroborated by short term observations of the estuarine sediment dynamics and transport during the monsoon, postmonsoon, summer and premonson seasons in Tirumalairajan River estuary.     

Evaluation of I-wall in New Orleans with back-calculated total stress soil parameters

This study back-calculated moduli and shear strength of soils in London Canal Ave., New Orleans, using full-scale load test data, and re-evaluated the behavior of the I-wall to explore how the existing levees and floodwalls may be reliably retrofitted and future levees and floodwalls may be designed. From the back-calculation, it turned out that the moduli of the field soils were mostly higher (1–12 times) than magnitudes appeared in Interagency Performance Evaluation Task Force (IPET). But the shear strength of a water-glazed Marsh layer in the gap turned out to be substantially lower (0.2–0.25 times) than the magnitude appeared in IPET. This much strength reduction was confirmed by field vane shear tests: tests with artificial water infiltration into the field vane hole presented immeasurably low disturbed strength and resulted in very high sensitivity that might contributed to the failure. This study also shows that the gap development and strength reduction in the water-glazed Marsh layer are two main causes of levee failure, which have been predicted in previous research. The stiffer-than-expected moduli of underlain layers did not affect the failure mechanism of the levee substantially because these underlain layers remained elastic. Therefore, retrofitting solutions should be the ones that may prevent the gap development and to reinforce the Marsh layer.     

A study on the sociospatial context of ethnic politics and entrepreneurial growth in Koreatown and Monterey Park

The study examines the various sociospatial features of immigrant populations in two transnationally-linked ethnic enclaves in terms of how they may facilitate and constrain the politics of growth and development. In recent decades, the growing ethnic enclave economies of Koreatown and Monterey Park have witnessed the emergence of progrowth ethnic interest groups comprised of immigrant capitalists, entrepreneurs, developers, and organizations, who are playing key roles in politically spearheading (re)development projects in the Los Angeles metropolitan area. Our aim is to understand how the sociospatial, entrepreneurial, and residential layout of these host municipalities set the context for the politics of growth in these ethnic enclave economies based on an analysis of GIS spatial mapping, 2000–2010 census data, and other secondary sources. The data suggests that Korean and Chinese elite face different political opportunities and challenges because of their different sociospatial characteristics—the former based on their greater entrepreneurial influence and weak electoral impact and the latter on their stronger political presence as residents.     

Vertical structure and microphysical characteristics of Typhoon Kompasu (2010) at landfall

The vertical structure and microphysics of Typhoon Kompasu that caused a lot of damage associated with strong winds and heavy rainfall over the Seoul metropolitan area on 1～2 September 2010 were examined primarily from wind profiler measurements. Four different periods that represent a stratiform, outer rainband, inner rainband, and eyewall region during passage of Typhoon Kompasu from 1200 to 2300 UTC 1 September were selected based on bright band intensities and vertical profiles of radar reflectivities and Doppler velocities. The bright band signatures observed in all of these periods indicated that the structure of Kompasu was basically stratiform in a weakening phase. Maximum rainfall rates up to 50 mm hr^?1 at the surface and mean wind speeds greater than 30 m s^?1 in the 2–4 km layer were observed in the eyewall region. Unlike the other regions that showed nearly zero vertical air motions or weak downdrafts below a melting layer, a mean updraft of ～1 m s^?1 was analyzed only in the eyewall region, which suggests that the updrafts may have enhanced drop growth that led to increasing surface rainfall rates. For each region, the vertical mean characteristics of rainfall parameters retrieved from wind profiler spectra below the melting layer were also examined. The rain properties between the inner and outer rainband were similar although they were apart with a distance of more than 100 km (> 2 hrs in time). The averaged mass-weighted mean diameters within the rainbands were larger than those in the stratiform and eyewall regions. A weaker bright band in the eyewall region suggests the presence of a relatively larger number of rimed particles associated with the updrafts around the melting layer. A stronger bright band was present in the rainbands, which indicates more active aggregation right above the melting layer.     

On the Mechanism of Air Pollutant Removal in Two-Dimensional Idealized Street Canyons: A Large-Eddy Simulation Approach

Flow resistance, ventilation, and pollutant removal for idealized two-dimensional (2D) street canyons of different building-height to street-width (aspect) ratios $AR$ are examined using the friction factor $f$ , air exchange rate (ACH), and pollutant exchange rate (PCH), respectively, calculated by large-eddy simulation (LES). The flows are basically classified into three characteristic regimes, namely isolated roughness, wake interference, and skimming flow, as functions of the aspect ratios. The LES results are validated by various experimental and numerical datasets available in the literature. The friction factor increases with decreasing aspect ratio and reaches a peak at $AR = 0.1$ in the isolated roughness regime and decreases thereafter. As with the friction factor, the ACH increases with decreasing aspect ratio in the wake interference and skimming flow regimes, signifying the improved aged air removal for a wider street canyon. The PCH exhibits a behaviour different from its ACH counterpart in the range of aspect ratios tested. Pollutants are most effectively removed from the street canyon with $AR = 0.5$ . However, a minimum of PCH is found nearby at $AR = 0.3$ , at which the pollutant removal is sharply weakened. Besides, the ACH and PCH are partitioned into the mean and turbulent components to compare their relative contributions. In line with our earlier Reynolds-averaged Navier–Stokes calculations (Liu et al., Atmos Environ 45:4763–4769, 2011), the current LES shows that the turbulent components contribute more to both ACH and PCH, consistently demonstrating the importance of atmospheric turbulence in the ventilation and pollutant removal for urban areas.