THE EFFECT OF MEAN CENTERING ON PREDICTION IN MULTIVARIATE CALIBRATION

Traditionally,one form of preprocessing in multivariate calibration methods such as principal componentregression and partial least squares is mean centering the independent variables(responses)and thedependent variables(concentrations).However,upon examination of the statistical issue of errorpropagation in multivariate calibration,it was found that mean centering is not advised for some datastructures.In this paper it is shown that for response data which(i)vary linearly with concentration,(ii)have no baseline(when there is a component with a non-zero response that does not change inconcentration)and(iii)have no closure in the concentrations(for each sample the concentrations of allcomponents add to a constant,e.g.100%)it is better not to mean center the calibration data.That is,the prediction errors as evaluated by a root mean square error statistic will be smaller for a model madewith the raw data than a model made with mean-centered data.With simulated data relativeimprovements ranging from 1% to 13% were observed depending on the amount of error in thecalibration concentrations and responses.     

EXAMINING LARGE DATABASES:A CHEMOMETRIC APPROACH USING PRINCIPAL COMPONENT ANALYSIS

Principal component analysis is used to examine large multivariate databases.The graphical approachto exploratory data analysis is described and illustrated with a single example of chemical compositiondata obtained on environmental dust particles.While the graphical approach to exploratory data analysishas certain advantages over the numerical procedures,the empirical approach described here should beviewed as complementary to the more robust treatments that statistical methodologies afford.     

Determination of the polynomial moments of the seismic moment rate density distribution with positivity constraints

We present a new formulation of the inverse problem of determining the temporal and spatial power moments of the seismic moment rate density distribution, in which its positivity is enforced through a set of linear conditions. To test and demonstrate the method, we apply it to artificial data for the great 1994 deep Bolivian earthquake. We use two different kinds of faulting models to generate the artificial data. One is the Haskell-type of faulting model. The other consists of a collection of a few isolated points releasing moment on a fault, as was proposed in recent studies of this earthquake. The positions of 13 teleseismic stations for which P - and SH -wave data are actually available for this earthquake are used. The numerical experiments illustrate the importance of the positivity constraints without which incorrect solutions are obtained. We also show that the Green functions associated with the problem must be approximated with a low approximation error to obtain reliable solutions. This is achieved by using a more uniform approximation than Taylor's series. We also find that it is necessary to use relatively long-period data first to obtain the low- (0th and 1st) degree moments. Using the insight obtained into the size and duration of the process from the first-degree moments, we can decrease the integration region, substitute these low-degree moments into the problem and use higher-frequency data to find the higher-power moments, so as to obtain more reliable estimates of the spatial and temporal source dimensions. At the higher frequencies, it is necessary to divide the region in which we approximate the Green functions into small pieces and approximate the Green functions separately in each piece to achieve a low approximation error. A derivation showing that the mixed spatio-temporal moments of second degree represent the average speeds of the centroids in the corresponding direction is given.     

METHODOLOGY: DISCRIMINANT FUNCTION ANALYSIS OF COMPOSITIONAL DATA: AN EXAMPLE FROM HYDRAULIC GEOMETRY

Many of the data sets analyzed by physical geographers are compositional in nature: they have row vectors that add to one (or 100%). These unit-sum constrained data sets should not be analyzed by standard multivariate statistical methods. Significant differences were found in the log-ratio mean vectors of the hydraulic exponents (which are unit-sum constrained) for two classes of streams: those with cohesive, non-vertical banks, and those with one firm and one loose bank. Compositional discriminant function analysis of bank stability on the basis of hydraulic geometry had a success rate of 88%, making routinely archived measurements of stream width, cross-sectional area, mean velocity, and discharge a readily available data base for predicting the stability of stream reaches. [Key words: geomorphology, hydraulic geometry, discriminant function, statistics.]     

SHORT COMMUNICATION THE RELATIONSHIP OF CLOSURE,MEAN CENTERING AND MATRIX RANK INTERPRETATION

This paper describes an investigation into the relationship of closure,a baseline offset and mean centeringto the interpretation of matrix rank.The equivalence of a certain type of closure to a constant baseline(i.e.a simple numerical offset which may vary between response channels but is constant over all samples)is demonstrated.A systematic approach to the interpretation of the rank of a matrix is given.     

EXPERIMENTAL DESIGN IN CHEMOMETRICS

Chemometrics is defined as the application of mathematical and statistical methods to chemical systems.Systems theory is seen to be useful for organizing and categorizing the inputs to and outputs fromchemical systems.Advances in measurement science in the 1950s and 1960s,particularly in analyticalchemistry,created a need for a multivariate approach to data analysis.Early chemometrics emphasizedthe use of structure-finding methods for existing data sets.In many instances,data sets can be obtainedfrom designed experiments.Such data sets are more likely to contain the desired information and the datacan usually be acquired at less cost.Renewed interest in statistical process control will provide many new,more robust data sets in the future.     

Complementary Use of Scalar,Directional, and Vector Statistics with an Application to Surface Winds

Vector data are not uncommon in geography, and include examples such as transportation flows, particulate transport, and cartographic distortion. The directional and vector means and variances of these types of data are easily computed using a complex-arithmetic extension of the equations for scalar mean and variance. The January surface wind field over the contiguous United States provides an example with which to compare the information provided by scalar, directional and vector-based statistics. Spatial patterns of the mean and variance of January wind velocity (the wind vector) resemble patterns of wind speeds and directions but are not a simple superposition of the two, and one cannot necessarily infer the nature of the velocity field from separately computed salar and directional statistics. However, scalar and directional means and variances can lend insight into the features contributing to the velocity mean and variance. Scalar, directional, and vector-based analyses thus provide complementary methods with which to examine the spatial patterns of wind, or of any flow field that can be represented as a vector.     

Complementary Use of Scalar,Directional, and Vector Statistics with an Application to Surface Winds

Vector data are not uncommon in geography, and include examples such as transportation flows, particulate transport, and cartographic distortion. The directional and vector means and variances of these types of data are easily computed using a complex-arithmetic extension of the equations for scalar mean and variance. The January surface wind field over the contiguous United States provides an example with which to compare the information provided by scalar, directional and vector-based statistics. Spatial patterns of the mean and variance of January wind velocity (the wind vector) resemble patterns of wind speeds and directions but are not a simple superposition of the two, and one cannot necessarily infer the nature of the velocity field from separately computed salar and directional statistics. However, scalar and directional means and variances can lend insight into the features contributing to the velocity mean and variance. Scalar, directional, and vector-based analyses thus provide complementary methods with which to examine the spatial patterns of wind, or of any flow field that can be represented as a vector.     

多元统计分析在分区研究中的应用

探讨了基于因子分析的聚类分析方法在遵循主要地理区划原则,特别是综合分析与主导因素相结合的原则和相对一致性原则过程中的特色。以中国土地利用程度和效益分区为例,首先利用因子分析对评价指标进行了降维处理,并研究了各个评价指标之间的关系;然后利用聚类分析,结合主要区划原则,将全国划分为5个类型区,12个亚区。     

地理学时空数据分析方法

随着地理空间观测数据的多年积累,地球环境、社会和健康数据监测能力的增强,地理信息系统和计算机网络的发展,时空数据集大量生成,时空数据分析实践呈现快速增长。本文对此进行了分析和归纳,总结了时空数据分析的7类主要方法,包括：时空数据可视化,目的是通过视觉启发假设和选择分析模型;空间统计指标的时序分析,反映空间格局随时间变化;时空变化指标,体现时空变化的综合统计量;时空格局和异常探测,揭示时空过程的不变和变化部分;时空插值,以获得未抽样点的数值;时空回归,建立因变量和解释变量之间的统计关系;时空过程建模,建立时空过程的机理数学模型;时空演化树,利用空间数据重建时空演化路径。通过简述这些方法的基本原理、输入输出、适用条件以及软件实现,为时空数据分析提供工具和方法手段。     

On the a priori estimation of collocation error covariance functions: a feasibility study

Error covariance estimates are necessary information for the combination of solutions resulting from different kinds of data or methods, or for the assimilation of new results in already existing solutions. Such a combination or assimilation process demands proper weighting of the data, in order for the combination to be optimal and the error estimates of the results realistic. One flexible method for the gravity field approximation is least-squares collocation leading to optimal solutions for the predicted quantities and their error covariance estimates. The drawback of this method is related to the current ability of computers in handling very large systems of linear equations produced by an equally large amount of available input data. This problem becomes more serious when error covariance estimates have to be simultaneously computed. Using numerical experiments aiming at revealing dependencies between error covariance estimates and given features of the input data we investigate the possibility of a straightforward estimation of error covariance functions exploiting known characteristics of the observations. The experiments using gravity anomalies for the computation of geoid heights and the associated error covariance functions were conducted in the Arctic region north of 64° latitude. The correlation between the known features of the data and the parameters variance and correlation length of the computed error covariance functions was estimated using multiple regression analysis. The results showed that a satisfactory a priori estimation of these parameters was not possible, at least in the area considered.     

中国高分辨率温度和降水模拟数据的验证

PRISM模型是一种基于地理特征和回归统计方法生成气候图的模型。基于中国及其周边国家地区2450多个气象台站观测数据,以PRISM模型模拟生成了中国2.5′×2.5′(≈4～5km)逐月温度和降水数据。利用独立于模拟数据的中国生态系统研究网络18个野外观测站的长年气候观测数据,检验了PRISM模型的模拟结果,表明PRISM模型较好地模拟了我国温度和降水的空间分布及季节变化,除了在高山和亚热带地区由于地表覆盖和局部地形的差异影响模拟结果,其模拟值与实测值之间的趋势线同1∶1线基本一致,具有显著相关关系,其中降水效果略差     

水文气象序列趋势分析与变异诊断的方法及其对比

日趋频繁的极端天气和水文事件对经济发展和人类生命安全构成重大危害,水文气象序列的趋势变化分析与预测研究是避免和控制这些破坏性全球环境变化的前提,也是目前亟待解决的科学问题之一。基于现代数学和统计学理论,气象学和水文学研究人员对水文气象要素趋势检验和突变点识别的方法做了大量的研究。针对当今普遍采用的参数统计、非参数秩检验和小波分析方法及其本质原理,在分类阐述的基础上,系统归纳总结了各个方法在应用过程中存在的问题及解决方案,并以黑河流域托勒气象站年平均气温为实例对比分析各方法计算结果的差异性,凝练出水文气象序列趋势分析与变异诊断的理论与方法系统体系,为今后理论方法的进一步改进及应用发展提供参考。     

Runoff Scaling in Large Rivers of the World

Runoff and precipitation scaling with respect to drainage area is analyzed for large river basins of the world, those with mean annual runoff in excess of 10 k³/yr. The usefulness of the specific runoff (runoff per unit drainage area, m/yr) to categorize runoff scaling laws across the complete spectrum of climatic and hydrologic conditions is evaluated. It is found that (1) runoff scales with drainage are in those river basins with specific runoff in excess of 0.15 m/yr (r² = 0.88); (2) runoff scaling with drainage area shows remarkably high statistical correlation (r²= 0.97) in river basins with specific runoff equal to or larger than 1.0 m/yr; (3) runoff does not Inc.rease with Inc.reasing drainage area in river basins with specific runoff below 0.15 m/yr, where no discernible statistical association was found between runoff and drainage area; and (4) precipitation depth (m/yr) is inversely proportional to drainage area raised to a fractional exponent in river basins with specific runoff in excess of 0.15 m/yr.     

近几十年来珠江三角洲1月和7月水位变异分析

以水动力学原理为基础,运用累积距平法、有序聚类分析法、滑动F识别与检验法和M-K趋势与突变分析法4种方法,对珠江三角洲1959-2005年47 a的7月和1月水位时间序列进行突变点分析.结果表明:7月平均高水位的变异点集中在1974-1982年和1989-1995年两个时段,1月平均低水位的变异点集中在1970-1980年和1984-1993年两个时段,且大部分潮位站存在一个变异点,少数存在两个.入海口门站1月平均低水位和7月平均高水位序列变异点前/后的均值出现增加的特征,1月平均低水位C1值基本保持不变     

风沙流中风速纵向脉动的实验研究

在4种风速条件下对风沙流中风速纵向脉动特性进行了风洞实验研究。研究发现，风速纵向脉动很大．不容忽视；脉动绝对大小随进口风速提高有增强趋势，随着高度的增加则变化不大；垂线脉动强度平均值随主流速度基本成正向线性关系；以脉动强度与当地风速之比表示的相对脉动强度随高度增加而降低，并且不同风速条件下相对脉动强度在床面附近相差较大，远离床面则趋向一致。另外，采用幂函数形式可较好地描述风沙流中平均风速的垂线分布。     

A STATISTICAL ANALYSIS OF THE FREEZE HAZARD IN NEW YORK STATE

Thirty years of data are examined for the last spring freeze and first autumn freeze at freeze thresholds of 0°C, -2.2°C, and -4.4°C. Four statistical conclusions of a 1958 Iowa freeze hazard study are tested in New York. The time series of freeze dates are random and normally distributed. Spring and autumn freeze dates are independent at a station. The variances of autumn freeze dates are homogeneous throughout New York and variances of spring freeze dates are homogeneous within each of three regions of similar climate. Statistical properties of the freeze date time series should be examined locally before results of studies in other regions are used. (Key words: freeze, frost, climatology, growing-season, New York, statistical methods.)     

巢湖沉积物粒度特征及其沉积学意义

对采自西巢湖湖心的一根长为143 cm的沉积柱进行了粒度分析,重建了粒度组成的演变过程。湖心沉积物主要为粉砂和黏土,粒度参数（平均粒径、标准偏差、偏度、尖度、分维值）分析表明沉积物分选程度较好,均为正偏态,峰态为很窄到非常窄,且具有一定的分形特征。C-M图解和概率累积曲线揭示了较弱的水动力环境,颗粒的搬运方式主要为跃移和悬移,比例分别约为70%和25%~30%。结合因子分析,识别出第一主因子（PC1）对细粒物质含量存在显著影响,其值反映了碎屑物质在湖泊中的搬运距离,PC1因子与平均粒径M_z可作为巢湖湖泊水位的替代性指标。     

Applicability of Kinetic Models for In Situ Combustion Processes with Different Oil Types

The in situ combustion (ISC) process is of interest as an enhanced oil recovery method because it is an alternative to traditional steam-based processes for heavy oil and bitumen recovery. ISC is a technique applicable outside the window of reservoir conditions deemed appropriate for steam injection (such as deeper and thinner reservoirs). The process involves complex chemical reactions and physical recovery mechanisms, and predicting the likelihood of successful ISC in field applications remains challenging. This paper describes a numerical investigation of the capability of different ISC kinetic models to predict the combustion behaviors of different types of oils (light oil, heavy oil, and bitumen). Three kinetic models (of Coats, Crookston, and Belgrave) were selected from literature and compared using data from four published combustion-tube experiments. The comparison procedure is as follows: (1) validate the numerical modeling of each kinetic model by matching the selected experimental results or duplicating the numerical results found in published literature; (2) adjust fluid viscosities and densities to match the fluid properties of each experiment;and (3) use each validated kinetic model to predict the performance of the other experiments without further tuning the kinetic parameters. The knowledge derived from the experiments provides guidance for choosing the appropriate kinetic model when no other data are available and for the preliminary design and screening study of a potential ISC project.