Two-stage permutation tests for determining homogeneity within a spatial cluster

The discovery of spatial clusters formed by proximal spatial units with similar non-spatial attribute values plays an important role in spatial data analysis. Although several spatial contiguity-constrained clustering methods are currently available, almost all of them discover clusters in a geographical dataset, even though the dataset has no natural clustering structure. Statistically evaluating the significance of the degree of homogeneity within a single spatial cluster is difficult. To overcome this limitation, this study develops a permutation test approach Specifically, the homogeneity of a spatial cluster is measured based on the local variance and cluster member permutation, and two-stage permutation tests are developed to determine the significance of the degree of homogeneity within each spatial cluster. The proposed permutation tests can be integrated into the existing spatial clustering algorithms to detect homogeneous spatial clusters. The proposed tests are compared with four existing tests (i.e., Park’s test, the contiguity-constrained nonparametric analysis of variance (COCOPAN) method, spatial scan statistic, and q-statistic) using two simulated and two meteorological datasets. The comparison shows that the proposed two-stage permutation tests are more effective to identify homogeneous spatial clusters and to determine homogeneous clustering structures in practical applications.     

Within versus between-lake variability of sedimentary diatoms: the role of sampling effort in capturing assemblage composition in environmentally heterogeneous shallow lakes

The effect of within-lake diatom assemblages variability on sample representativity and its subsequent impact on between-lake comparisons were addressed in three environmentally heterogeneous shallow lakes from the Argentinean Pampas. Surface sediment samples were collected from the open waters and the highly vegetated littoral areas on a seasonal basis and analyzed for diatom assemblages composition. Within-lake variability was assessed by comparing the Bray Curtis distances between original data and the Monte Carlo-simulated average assemblages composition through non-metric multidimensional scaling (NMDS). Diatom assemblages showed a high variability in composition, evidencing large dispersions of samples around the centroid in NMDS plots. Permutational multivariate analysis of variance tests signaled significant differences in average composition between the three lakes, related mainly to their differences in conductivity and depth. Representativity of original samples was assessed through principal coordinates analyses ordinations of the three lakes, being samples lying in the overlapping areas of the plot classified as poor representatives of between-lake differences. Several samples, both from littoral and open waters, were classified as poor representatives through this method. Simulation allowed us to evaluate the effect of sample replication on improving between-lake comparisons, and showed that collecting two littoral and two open-water samples allowed us to faithfully capture differences in average composition among the three lakes. Hence, the results suggest that using a single sample to estimate diatom assemblages composition in these lakes should be avoided, as it fails to capture between-lake differences, leading to biases in compositional comparisons among lakes and regions. Consequently, including multiple samples from each lake when constructing calibration sets would be the best option to obtain reliable paleoenvironmental reconstructions from single sediment cores in these environmentally heterogeneous shallow lakes.     

Quantification of Uncertainty in Ore-Reserve Estimation: Applications to Chapada Copper Deposit,State of Goiás,Brazil

Ordinary kriging (OK) has been used widely for ore-reserve estimation because of its superior characteristics in relation to other methods. One of these characteristics is related to the quantification of uncertainty by the kriging variance. However, the kriging variance does not recognize local data variability, which is an important issue in the process of ore-reserve estimation, when heterogeneous mineral deposits with richer and poorer parts are being evaluated. This paper proposes the use of interpolation variance as a reliable measure of local data variability and, therefore, adequate for ore-reserve classification. With a reliable measurement of data variability, local confidence can be calculated using the classical confidence interval around an estimate. Errors derived from local confidence then are used to assign classes according to a degree of certainty within some confidence level. Comparative tests using both OK variance and interpolation variance are carried out using exploration data from Chapada Copper Deposit, State of Goiás, Brazil. Results show that the interpolation variance provides a better way to measure uncertainty and consequently to classify reserves.     

用树轮灰度重建乌孙山北坡4—5月平均最低气温

利用2006年采自新疆伊犁乌孙山北坡3个采点的树轮样本,建立了树轮宽度年表,采用树轮图像分析法进一步建立了3种宽度年表和5种灰度年表。相关分析发现,在所有参数年表中乌孙山北坡3个树轮标准化全轮灰度年表序列与该地区4—5月平均最低气温显著相关,相关系数最大可达-0.552。经多方面检验可知,利用树轮标准化全轮灰度年表重建该地区过去324 a 的4—5月最低气温是可信的。通过对重建最低气温序列进行功率谱分析发现乌孙山北坡4—5月最低气温具有31 a、36 a和48 a的变化准周期;小波分析证实,31~32 a的低频变化周期最为显著,1800年以前,震荡随时间推移逐渐减弱,周期逐渐缩短,19世纪后期震荡加强,进入20世纪,震荡减弱,逐渐趋于稳定。4—5月平均最低气温经历了11高11低的变化阶段。     

STATISTICAL F-TESTS FOR ABSTRACT FACTOR ANALYSIS AND TARGET TESTING

Fisher variance ratio tests are developed for determining(1)the number of statistically significantabstract factors responsible for a data matrix and(2)the significance of target vectors projected into theabstract factor space.F-tests,developed from the viewpoint of vector distributions,are applied tovarious data sets taken from the chemical literature.     

A TEST OF SIGNIFICANCE FOR PARTIAL LEAST SQUARES REGRESSION

Partial least squares (PLS) regression is a commonly used statistical technique for performingmultivariate calibration, especially in situations where there are more variables than samples. Choosingthe number of factors to include in a model is a decision that all users of PLS must make, but iscomplicated by the large number of empirical tests available. In most instances predictive ability is themost desired property of a PLS model and so interest has centred on making this choice based on aninternal validation process. A popular approach is the calculation of a cross-validated r~2 to gauge howmuch variance in the dependent variable can be explained from leave-one-out predictions. Using MonteCarlo simulations for different sizes of data set, the influence of chance effects on the cross-validationprocess is investigated. The results are presented as tables of critical values which are compared againstthe values of cross-validated r~2 obtained from the user's own data set. This gives a formal test forpredictive ability of a PLS model with a given number of dimensions.     

Spatial variability in surface sediment composition characterised by near-infrared (NIR) reflectance spectroscopy

Near-infrared (NIR) spectral data were obtained from 165 surface sediment samples from a northern Swedish humic, mesotrophic lake (0.5 km2). The NIR spectra, together with data on water depth and loss-on-ignition (LOI), allow an evaluation of the source of spatial variance in sediment characteristics. The results show that water depth and organic matter (LOI) account for 20 and 16%, respectively, of the variance in the NIR-absorbance data. More importantly, the spatial variance in the spectral data suggest that NIR analysis of lake sediments mainly reflect sediment properties that cannot simply be explained by depth or amount of organic matter. The influence of inlets and land-use (e.g. clear-cutting) on sediment characteristics was more pronounced in the spectral data than would be expected from the LOI data. This is explained by differences in the chemical composition of the organic matter, as revealed by NIR spectroscopy, rather than in the amount of organic matter or depth-related sedimentation properties (e.g. particle size or density). This initial attempt to characterise sediment properties using NIR suggests that NIR analysis might become a valuable complementary tool to traditional sediment characterisation.     

香港降水的短期气候预测

利用正规化周期回归分析方法和门限自回归理论对香港1853-1995年月降水资料进行了建模和拟合，并对1996年进行了预报试验，正规化周期回归拟合效果较好，对香港7个时距的试报准确率为71%，建立了7个时距的10年滑动平均序列的门限自回归模型，模型对序列拟合效果较理想，预报误差较小，试报准确率主国100%。     

Water chemistry of some karst environments in Norway

In August 1983, 18 samples were collected in Norwegian karst environments: seepage waters, surface flow upstream sinkholes or caves, allogenic and authigenie karst springs. Hydrochemical data (ion contents and computed variables for CO-CaCO system) are described by means of a factor analysis, the principal components analysis. Four factors, responsible for about 90 % of the total variance, are extracted and interpreted. Five clusters of samples are then identified:

– Authigenic karst waters (seepage and only carbonate aquifer);

– Waters of very short residence time (surface or karst flow);

– CO-rich waters (seepage and possibly organic-rich surface waters), CO2 part is discussed in more detail;

– CO-poor waters (surface waters above tree-line);

– a central group, combining 2 or more of these characters.     

GIS‐based multicriteria spatial modeling generic framework

Multicriteria analysis is a set of mathematical tools and methods allowing the comparison of different alternatives according to many criteria, often conflicting, to guide the decision maker towards a judicious choice. Multicriteria methods are used in spatial context to evaluate and compare spatial decision alternatives, often modeled through constraint‐based suitability analysis and represented by point, line, and polygon features or their combination, and evaluated on several space‐related criteria, to select a restricted subset for implementation. Outranking methods, a family of multicriteria methods, may be useful in spatial decision problems, especially when ordinal evaluation criteria are implied. However, it is recognized that these methods, except those devoted to multicriteria classification problems, are subject to computational limitations with respect to the number of alternatives. This paper proposes a framework to facilitate the incorporation and use of outranking methods in geographical information systems (GIS). The framework is composed of two phases. The first phase allows producing a planar subdivision of the study area obtained by combining a set of criteria maps; each represents a particular vision of the decision problem. The result is a set of non‐overlapping spatial units. The second phase allows constructing decision alternatives by combining the spatial units. Point, line and polygon feature‐based decision alternatives are then constructed as an individual, a grouping of linearly adjacent or a grouping of contiguous spatial units. This permits us to reduce considerably the number of alternatives, enabling the use of outranking methods. The framework is illustrated through the development of a prototype and through a step‐by‐step application to a corridor identification problem. This paper includes also a discussion of some conceptual and technical issues related to the framework.     

FACTOR ANALYSIS OF A SIMULATED DATA MATRIX INVOLVING AQUEOUS COMPLEX EQUILIBRIA

Abstract factor analyses were performed on databases consisting of simulated samples from aqueousequilbria.The program COMPLEX was used to generate equilibrium species in a system of three reactantmetals and five reactant bases.Reactant concentrations and pH were drawn from random-normaldistributions so that sample data vectors comprised a multivariate log-normal distribution of equilibriumconcentrations.In addition,sample groups were created containing different distributions for pH andreactant concentrations.Equilibrium species were shown to contain variance contributed by change in pH among samples aswell as change in reactant concentrations.Factor modelling revealed the qualitative relationships amongthe species and how the relationships change with pH.Factors also revealed those reactants containingvariance in the data matrix.In some cases,reactant variance obscured relationships between pH and theequilibrium species.Since factor modelling of a simulated data matrix revealed the expected chemical equilibriuminteractions,a potentially powerful tool exists for investigating the effects of outliers and error.     

Relatedness between contemporary and subfossil cladoceran assemblages in Turkish lakes

Cladocerans are valuable indicators of environmental change in lakes. Their fossils provide information on past changes in lake environments. However, few studies have quantitatively examined the relationships between contemporary and sub-fossil cladoceran assemblages and no investigations are available from Mediterranean lakes where salinity, eutrophication and top-down control of large-bodied cladocerans are known to be important. Here we compared contemporary Cladocera assemblages, sampled in summer, from both littoral and pelagic zones, with their sub-fossil remains from surface sediment samples from 40 Turkish, mainly shallow, lakes. A total of 20 and 27 taxa were recorded in the contemporary and surface sediment samples, respectively. Procrustes rotation was applied to both the principal components analysis (PCA) and redundancy analysis (RDA) ordinations in order to explore the relationship between the cladoceran community and the environmental variables. Procrustes rotation analysis based on PCA showed a significant accord between both littoral and combined pelagic–littoral contemporary and sedimentary assemblages. RDA ordinations indicated that a similar proportion of variance was explained by environmental variation for the contemporary and fossil Cladocera data. Total phosphorus and salinity were significant explanatory variables for the contemporary assemblage, whereas salinity emerged as the only significant variable for the sedimentary assemblage. The residuals from the Procrustes rotation identified a number of lakes with a high degree of dissimilarity between modern and sub-fossil assemblages. Analysis showed that high salinity, deep water and high macrophyte abundance were linked to a lower accord between contemporary and sedimentary assemblages. This low accord was, generally the result of poor representation of some salinity tolerant, pelagic and macrophyte-associated taxa in the contemporary samples. This study provides further confirmation that there is a robust relationship between samples of modern cladoceran assemblages and their sedimentary remains. Thus, sub-fossil cladoceran assemblages from sediment cores can be used with confidence to track long-term changes in this environmentally sensitive group and in Mediterranean lakes, subjected to large inter-annual variation in water level, salinity and nutrients.     

DISCRIMINANT PRINCIPAL COMPONENTS ANALYSIS

When the number of variables exceeds the number of samples, one method of multivariate discriminationis to use principal components analysis to reduce the dimensionality and then to perform canonicalvariates analysis (PC-CVA). This paper proposes an alternative approach in which discriminant analysisis carried out by a weighted principal component analysis of the group means (DPCA). This method doesnot require prior data reduction and produces discriminant factors that are orthogonal in the original dataspace. The theory and performance of the two methods are compared. Although the individual factors ofDPCA are found to be less discriminating than PC-CVA, the overall discrimination, calculated bymultivariate analysis of variance, and the predictive value, estimated by the leaving-one-out error rate,are broadly comparable.     

Assessment of freshwater diatoms as quantitative indicators of past climatic change in the Yukon and Northwest Territories,Canada

We identified, enumerated, and interpreted the diatom assemblages preserved in the surface sediments of 59 lakes located between Whitehorse in the Yukon and Tuktoyaktuk in the Northwest Territories (Canada). The lakes are distributed along a latitudinal gradient that includes several ecoclimatic zones. It also spans large gradients in limnological variables. Thus, the study lakes are ideal for environmental calibration of modern diatom assemblages. Canonical correspondence analysis, with forward selection and Monte Carlo permutation tests, showed that maximum lake depth and summer surface-water temperature were the two environmental variables that accounted for most of the variance in the diatom data. The concentrations of sodium and calcium were also important explanatory variables. Using weighted-averaging regression and calibration techniques, we developed a predictive statistical model to infer lake surface-water temperature, and we evaluated the feasibility of using diatoms as paleoclimate proxies. This model may be used to derive paleotemperature inferences from fossil diatom assemblages at appropriate sites in the western Canadian Arctic.     

新疆渭干河流域地下水含盐量的时空变异特征

对面积约3 408 km²的渭干河流域地下水含盐量进行取样检测,应用地质统计学方法对取得数据进行了半方差函数分析。结果表明,该地区1998、1999年地下水含盐量变异函数曲线的理论模型符合球状模型;1997年、2000年地下水含盐量变异函数曲线的理论模型符合有基台线性模型。通过对1997年、1998年、1999年及2000年水样的分析,得出该地区地下水含盐量在时间与空间上皆存在明显变异性的结论。在空间尺度上,地下水含盐量从研究区的西北向东南方向有增加的趋势。从整体上看,研究区地下水含盐量东部高于西部;南部高于北部;东南部高于西北部。在时间尺度上,研究区东南部地下水随着时间的推移正向盐渍化加重方向发展。本文利用软件Geopack与Surfer7.0软件绘制了地下水含盐量的时空分布图,为该地区地下水盐分的管理与今后的防止盐渍化提供了决策依据。     

Multivariate Statistical Analysis and Geochemical Modeling to Characterize the Surface Water of Oued Chemora Basin,Algeria

Multivariate statistical methods and inverse geochemical modeling were jointly used to deduce the genetic origin of chemical parameters of surface water in the Oued Chemora Basin. The analysis of variance indicates that variations of all parameters at the three stations are significant except for pH and T (p > 0.05). R-mode cluster analysis reveals two distinct groups at each station and led to the conclusion that the major ion chemistry in the three stations is derived from organic and artificial fertilizers due to agricultural activities in the area and water–rock interaction. Mineral saturation indices, calculated from major ions, indicate that the surface water is generally super-saturated with carbonate phases, and all the water samples are under-saturated with respect to gypsum, halite, and CO_2(g). In a broad sense, the reactions responsible for the hydrochemical evolution in the Basin fall into three categories: (1) dissolution of evaporite minerals; (2) precipitation of carbonate minerals; and (3) ion exchange.     

Scale variance analysis coupled with Moran's I scalogram to identify hierarchy and characteristic scale

Scale variance is highly sensitive to multi-scale patterns of variables, which is advantageous in identifying spatial hierarchy and characteristic scale(s). However, the significance of peak(s) in scale variance cannot be statistically tested, and different spatial patterns may be obtained when different zoning systems are used to calculate scale variance. To address these two problems, this study compared the scale levels with peaks in scale variance and the scale levels at which there were breaks in the nature of spatial autocorrelation as identified by shifts in Moran's I scalogram. The estimates for three simulated landscapes showed that accordance between scale levels identified employing the two methods can be used to evaluate the significance of peaks in scale variance and choose a more reasonable zoning system. The approach of scale variance analysis coupled with Moran's I scalogram was also applied to the Xilin River Basin of Inner Mongolia, China. The most vital characteristic scale (64 × 32 km) identified for the growing-season net ecosystem productivity (NEP) of the basin was validated by other spatial pattern analysis methods such as semi-variogram, Moran's I correlogram, and wavelet variance analyses, and the directionality of the chosen zoning systems was found to be similar to the orientation of actual dominant vegetation type patches. The results demonstrate that Moran's I scalogram can be used to improve the interpretation of the results of scale variance analysis and increase the reliability of scale variance analysis for landscapes having a repetitive patch pattern or gradient variation and that the proposed approach is suitable for identifying the hierarchy and the characteristic scales of patterns or processes. In summary, this study used a simple approach to solve two problems in scale variance analysis, thereby improving the methodology and enhancing the theoretical basis of multi-scale analysis.     

Geospatial spreadsheets with microscale air quality visualization and synchronization for supporting multiple-scenario visual collaboration

A major obstacle of the interdisciplinary communications for decision-making is that each participant prefers the solution from their own area because current collaboration systems cannot effectively mediate among many alternatives. If a visual collaboration system could display multiple alternatives in a single visual presentation, users would be able to compare alternatives with only a few variables, where all other parameters are fixed, at least from a visual perspective. In this study, we developed a visualization tool to support a microscale air quality (MSAQ) management group, the members of which often need to compare the effects of many alternative control methods. The main achievements of this study are: (1) three-dimensional (3D) visualization of the MSAQ using a 3D city model and (2) development of a geospatial spreadsheet (GS) to facilitate visual comparisons, thereby improving decision-making by making it easy to compare differences based on realistic visual display items. A questionnaire-based survey showed that use of the GS could generate a shared perspective and provide a spatiotemporal context for the participants, thereby making it easy to compare, mediate and reach decisions when confronted with many alternatives.     

Use of a Probabilistic Neural Network to Reduce Costs of Selecting Construction Rock

Rocks used as construction aggregate in temperate climates deteriorate to differing degrees because of repeated freezing and thawing. The magnitude of the deterioration depends on the rock's properties. Aggregate, including crushed carbonate rock, is required to have minimum geotechnical qualities before it can be used in asphalt and concrete. In order to reduce chances of premature and expensive repairs, extensive freeze-thaw tests are conducted on potential construction rocks. These tests typically involve 300 freeze-thaw cycles and can take four to five months to complete. Less time consuming tests that (1) predict durability as well as the extended freeze-thaw test or that (2) reduce the number of rocks subject to the extended test, could save considerable amounts of money. Here we use a probabilistic neural network to try and predict durability as determined by the freeze-thaw test using four rock properties measured on 843 limestone samples from the Kansas Department of Transportation. Modified freeze-thaw tests and less time consuming specific gravity (dry), specific gravity (saturated), and modified absorption tests were conducted on each sample. Durability factors of 95 or more as determined from the extensive freeze-thaw tests are viewed as acceptable—rocks with values below 95 are rejected. If only the modified freeze-thaw test is used to predict which rocks are acceptable, about 45% are misclassified. When 421 randomly selected samples and all four standardized and scaled variables were used to train aprobabilistic neural network, the rate of misclassification of 422 independent validation samples dropped to 28%. The network was trained so that each class (group) and each variable had its own coefficient (sigma). In an attempt to reduce errors further, an additional class was added to the training data to predict durability values greater than 84 and less than 98, resulting in only 11% of the samples misclassified. About 43% of the test data was classed by the neural net into the middle group—these rocks should be subject to full freeze-thaw tests. Thus, use of the probabilistic neural network would meanthat the extended test would only need be applied to 43% of the samples, and 11% of the rocks classed as acceptable would fail early.     

Geochemical Characterization of Surface Water and Groundwater in Soummam Basin,Algeria

Multivariate statistical methods and geochemical modeling were used to assess spatial variation of water quality of the Soummam basin, Algeria. The application of hierarchical cluster analysis (HCA) showed three main groups of samples. Group 1 samples are exclusively composed of surface water. Groups 2 and 3 samples consist of groundwater. Discriminant analysis assigned about 98.6% of the cases grouped by HCA. All groups are super-saturated with Ca-montmorillonite, dolomite, gibbsite, K-mica, kaolinite, and quartz, and all these groups are under-saturated with albite, anhydrite, anorthite, CO_2(g), gypsum, halite, melanterite, and smithsonite. The results of analysis of variance indicate that the saturation indices of each of the mineral phases are significant except for chalcedony and quartz (p > 0.05). The results obtained by inverse geochemical modeling show the dissolution of albite, which justifies Na enrichment during the chemical evolution of groundwater. Calcite, dolomite, Ca-montmorillonite, kaolinite, illite, gibbsite, and K-mica are shown to have always precipitated.