Simultaneous estimation of cross-validation errors in least squares collocation applied for statistical testing and evaluation of the noise variance components

The cross-validation technique is a popular method to assess and improve the quality of prediction by least squares collocation (LSC). We present a formula for direct estimation of the vector of cross-validation errors (CVEs) in LSC which is much faster than element-wise CVE computation. We show that a quadratic form of CVEs follows Chi-squared distribution. Furthermore, a posteriori noise variance factor is derived by the quadratic form of CVEs. In order to detect blunders in the observations, estimated standardized CVE is proposed as the test statistic which can be applied when noise variances are known or unknown. We use LSC together with the methods proposed in this research for interpolation of crustal subsidence in the northern coast of the Gulf of Mexico. The results show that after detection and removing outliers, the root mean square (RMS) of CVEs and estimated noise standard deviation are reduced about 51 and 59%, respectively. In addition, RMS of LSC prediction error at data points and RMS of estimated noise of observations are decreased by 39 and 67%, respectively. However, RMS of LSC prediction error on a regular grid of interpolation points covering the area is only reduced about 4% which is a consequence of sparse distribution of data points for this case study. The influence of gross errors on LSC prediction results is also investigated by lower cutoff CVEs. It is indicated that after elimination of outliers, RMS of this type of errors is also reduced by 19.5% for a 5 km radius of vicinity. We propose a method using standardized CVEs for classification of dataset into three groups with presumed different noise variances. The noise variance components for each of the groups are estimated using restricted maximum-likelihood method via Fisher scoring technique. Finally, LSC assessment measures were computed for the estimated heterogeneous noise variance model and compared with those of the homogeneous model. The advantage of the proposed method is the reduction in estimated noise levels for those groups with the fewer number of noisy data points.     

Temporal variability in summertime bottom hypoxia in shallow areas of Mobile Bay,Alabama

This paper addresses temporal variability in bottom hypoxia in broad shallow areas of Mobile Bay, Alabama. Time-series data collected in the summer of 2004 from one station (mean depth of 4 m) exhibit bottom dissolved oxygen (DO) variations associated with various time scales of hours to days. Despite a large velocity shear, stratification was strong enough to suppress vertical mixing most of the time. Bottom DO was closely related to the vertical salinity gradient (ΔS). Hypoxia seldom occurred when ΔS (over 2.5 m) was <2 psu and occurred almost all the time when ΔS was >8 psu in the absence of extreme events like hurricanes. Oxygen balance between vertical mixing and total oxygen demand was considered for bottom water from which oxygen demand and diffusive oxygen flux were estimated. The estimated decay rates at 20°C ranging between 0.175–0.322 d⁻¹ and the corresponding oxygen consumption as large as 7.4 g O₂ m⁻² d⁻¹ fall at the upper limit of previously reported ranges. The diffusive oxygen flux and the corresponding vertical diffusivity estimated for well mixed conditions range between 8.6–9.5 g O₂ m⁻² d⁻¹ and 2.6–2.9 m² d⁻¹, respectively. Mobile Bay hypoxia is likely to be associated with a large oxygen demand, supported by both water column and sediment oxygen demands, so that oxygen supply from surface water during destratification events would be quickly exhausted to return to hypoxic conditions within a few hours to days after destratification events are terminated.     

Gravimetry on the Erimo Seamount, Japan

A gravimetric survey on the sea-bottom was performed on the Erimo Seamount by the French submersible “Nautile”. It took place during the second phase of the Kaiko French-Japanese Program. The reference station was established on the Erimo submarine observatory at a depth of 3942 m and from this point the survey of four stations was carried out. The obtained accuracy of the gravity field measurements was about 0.1 mGal.

A three-dimensional model of the seamount and its surroundings was constrained by the free-air anomaly values from the sea surface and from the sea bottom and by the perfect Seabeam topography survey of the whole area. The model which fitted the observed values best, allowed us to identify a low-density layer of coral limestones and volcaniclastics capping the seamount and to define the geometry of the interface between basalts and coral rocks.     

Geochemical characteristics of island-arc volcanic rocks in the Nan-Nam Pat-Phetchabun zone,northern Thailand

Late Permian-Early Triassic (P₂-T₁) volcanic rocks distributed on the eastern side of ocean-ridge and oceanic-island basalts in the Nan-Uttaradit zone were analyzed from aspects of petrographic characteristics, rock assemblage, REE, trace elements, geotectonic setting, etc., indicating that those volcanic rocks possess the characteristic features of island-arc volcanic rocks. The volcanic rock assemblage is basalt-basaltic andesite-andesite. The volcanic rocks are sub-alkaline, dominated by calc-alkaline series, with tholeiite series coming next. The chemical composition of the volcanic rocks is characterized by low TiO₂ and K₂O and high Al₂O₃ and Na₂O. Their REE patterns are of the flat, weak LREE-enrichment right-inclined type. The trace elements are characterized by the enrichment of large cation elements such as K, Rb and Ba, common enrichment of U and Th, and depletion of Nb, Ta, Zr and Hf. The petrochemical plot falls within the field of volcanic rocks, in consistency with the plot of island-arc volcanic rocks in the Jinsha River zone of China. This island-arc volcanic zone, together with the ocean-ridge/oceanic island type volcanic rocks in the Nan-Uttaradit zone, constitutes the ocean-ridge volcanic rock-island-arc magmatic rock zones which are distributed in pairs, indicating that the oceanic crust of the Nan-Uttaradit zone once was of eastward subduction. This work is of great significance in exploring the evolution of paleo-Tethys in the Nan-Uttaradit zone.     

Assessment of three temperature reconstruction methods in the virtual reality of a climate simulation

The performance of statistical climate reconstruction methods in the pre-instrumental period is uncertain, as they are calibrated in a short instrumental period but applied to much longer reconstructions time spans. Here, the virtual reality created by a climate simulation of the past millennium with the model ECHO-G is used as a test bed of three methods to reconstruct the annual Northern Hemisphere temperature. The methods are Composite plus Scaling, the inverse regression method of Mann et al. (Nature 392:779–787, 1998) and a direct principal-components regression method. The testing methodology is based on the construction of pseudo-proxies derived from the climate model output, the application of each of these methods to pseudo-proxy timeseries, and the comparison of their result with the simulated mean temperature. Different structures of the noise have been used to construct pseudo-proxies, ranging from the simulated grid-point precipitation. Also, one sparse and one denser pseudo-proxy network, co-located with two real networks, have been considered. All three methods underestimate the simulated variations of the Northern Hemisphere temperature, but the Composite plus Scaling method clearly displays a better performance and is robust against the different noise models and network size. The most relevant factor determining the skill of the reconstruction appears to be the network size, whereas the different noise models tend to yield similar results.     

Segmentation algorithm for long time series analysis

Time series analysis is an important issue in the earth science-related engineering applications such as hydrology, meteorology and environmetrics. Inconsistency and nonhomogeneity that might arise in a time series yield segments with different statistical characteristics. In this study, an algorithm based on the first order statistical moment (average) of a time series is developed and applied on five time series with length ranging from 84 items to nearly 1,300. Comparison to the existing segmentation algorithms proves the applicability and usefulness of the proposed algorithm in long hydrometeorological and geophysical time series analysis.     

Colloidal Stability and Toxicity of Gold Nanoparticles and Gold Chloride on <Emphasis Type="Italic">Chlamydomonas reinhardtii</Emphasis>

Here we have examined interactions of gold nanoparticles differing in primary particle size and coating with the green algae Chlamydomonas reinhardtii as function of the colloidal stability of the particles in the experimental media used for toxicity studies. Interactions of dissolved Au³⁺ ions with algae were also examined. Included endpoints were photosynthetic yield and algal growth. Morphological and structural effects were examined microscopically and by flow cytometry. The results indicate no significant toxicity of gold nanoparticles to C. reinhardtii. Analysis of published data suggests toxicity of gold nanoparticles on algal growth to relate rather to particular coatings than to the gold core.     

Hydrochemical and Multivariate Statistical Evaluation of Heavy Metals in Shallow Alluvial Aquifers of North Brahmaputra Plain,India

The aim of this study was to display distribution and relationships of heavy elements in the unconfined, shallow alluvial aquifers of the lower Jia Bharali catchment and adjoining areas in central part of North Brahmaputra Plain (NBP), India using hydrochemical as well as multivariate statistical techniques such as principal component analysis (PCA) and cluster analysis. The original matrix was made up of 10 trace elements (As, Cd, Cu, Co, Cr, Fe, Mn, Pb, Ni and Zn) estimated from 50 shallow alluvial dug wells in both the wet and the dry season for a duration of 3 hydrological years (2008–2011). Except As, Cu and Zn all the other toxic metals in the shallow aquifers were found exceeding the WHO maximum permissible limits for drinking water. PCA extracted five varimax factors as geogenic, agricultural and anthropogenic explaining about 71.2% of the total variance in the wet season and 69.3% total variance in the dry season. Hierarchical cluster analysis classified the dug wells into two groups in the wet season and three groups in the dry season with respect to the heavy elements. The results emphasized the need for routine monitoring and management in order to avoid contamination of groundwater sources in the NBP with respect to the dissolved trace elements.     

Development and verification of the comprehensive model for physical properties of hydrate sediment

Natural gas hydrate is widely distributed all over the world and may be a potential resource in the near future, whereas hydrate dissociation during the development affects wellbore stability and drilling safety. However, the present modeling of hydrate reservoir parameters ignored the influence of effective stress and only considered the hydrate saturation. In this paper, a series of stress sensitivity experiments for the unconsolidated sandstone were carried out, and the influence of mean effective stress on physical parameters was obtained; a comprehensive model for the physical parameters of hydrate reservoir was developed subsequently. With the help of ABAQUS finite element software, the established comprehensive model was verified by the use of the wellbore stability numerical model of hydrate reservoir. The verification results show that ignoring the effect of mean effective stress on the parameters of hydrate formation aggravates the invasion of drilling fluid into the hydrate formation. Besides, ignoring the stress sensitivity of reservoir physical parameters will underestimate the wellbore instability during hydrate drilling, which will be a threat to the safety of gas hydrate drilling. At the end of the drilling operation, the maximum plastic strain of the model for considering and not considering stress sensitivity was 0.0145 and 0.0138, respectively. Therefore, the established comprehensive model will provide a theoretical support for accurately predicting the engineering geological disasters in hydrate development process.     

Assessing desertification by using soil indices

Desertification generally refers to land degradation in arid, semiarid, and dry semi-humid climatic zones. It involves five principal processes: vegetation degradation, water erosion, wind erosion, salinization and waterlogging, and soil crusting and compaction. The aim of this study is assessing desertification using soil criteria. For this purpose, nine indices including sodium absorption ratio (SAR), soil gypsum percentage, soil texture, the content of HCO₃ ^?, the percentage of the organic matter, electrical conductivity (EC), pH, the content of the soil sodium, and chloride were used. The soil samples were taken in the north of Zayandeh-Rood River in Isfahan province of Iran, using soil data randomly sampled in a depth of 0–20 cm. After assessing the normality of the samples using Kolmogorov-Smirnov test, indices were imported into GIS environment and interpolated with IDW and normal and discrete kriging methods for delineating soil characteristics maps based on MEDALUS model. In this model, the data were firstly changed from 100 to 200. Thus 100 and 200 are estimated as the best and worst quality, respectively. Then the final map of soil criteria has been created by geometric mean of its indicators. The results showed that the maximum area is related to the medium class of desertification and is equal to 44,746 ha. The areas of severe and very severe classes of desertification are equal to 30,949 and 351 ha, respectively. The results also revealed that the indices of the organic matter and soil gypsum percentage are the most influential indices which affect desertification phenomenon.