梯级-关联算法原理及其在月流量预报中的应用

传统BP网络需要预先设定网络隐含层的层数和每层的节点数,使得在预测过程中难以确定网络的最优结构。与之相反,梯级-关联算法(CC)要求初始网络仅含有输入层和输出层,通过运算不断向网络增加隐含节点。在介绍梯级-关联算法原理的基础上,分别运用梯级-关联算法和BP算法对拉萨河拉萨站的月流量进行了预测,结果显示:在不损失预测精度的前提下,梯级-关联算法的运算次数仅为5次,而BP算法则需要运算70 000次,运算效率有很大的提高,同时网络的规模也有所减小。     

A comparison between cokriging and ordinary kriging: Case study with a polymetallic deposit

Cokriging is applied to the estimation of mineral resources in a polymetallic deposit. Several major steps, which should be taken in using cokriging, are highlighted as necessary practical considerations. The case study is related to an ultramafic copper-nickel deposit. Six elements, Cu, Ni, Au, Ag, Pt, and Pd, occurring in the deposit, are partitioned into three subgroups and the elements within each group are simultaneously estimated on the basis of over 4000 drill assays. A comparison was made between ordinary kriging and cokriging methods through cross-validation. The results show that cokriging has significantly improved the estimates of resources by reducing the overall estimation error by over 15% and the variance of error by over 20%.     

A new form of the cokriging equations

Myers developed a matrix form of the cokriging equations, but one that entails the solution of a large system of linear equations. Large systems are troublesome because of memory requirements and a general increase in the matrix condition number. We transform Myers’s system into a set of smaller systems, whose solution gives the classical kriging results, and provides simultaneously a nested set of lower dimensional cokriging results. In the course of developing the new formulation we make an interesting link to the Cauchy-Schwarz condition for the invertibility of a system, and another to a simple situation of coregionalization. In addition, we proceed from these new equations to a linear approximation to the cokriging results in the event that the crossvariograms are small, allowing one to take advantage of a recent results of Xie and others which proceeds by diagonalizing the variogram matrix function over the lag classes.     

Pseudo-cross variograms, positive-definiteness, and cokriging

Cokriging allows the use of data on correlated variables to be used to enhance the estimation of a primary variable or more generally to enhance the estimation of all variables. In the first case, known as the undersampled case, it allows data on an auxiliary variable to be used to make up for an insufficient amount of data. Original formulations required that there be sufficiently many locations where data is available for both variables. The pseudo-cross-variogram, introduced by Clark et al. (1989), allows computing a related empirical spatial function in order to model the function, which can then be used in the cokriging equations in lieu of the cross-variogram. A number of questions left unanswered by Clark et al. are resolved, such as the availability of valid models, an appropriate definition of positive-definiteness, and the relationship of the pseudo-cross-variogram to the usual cross-variogram. The latter is important for modeling this function.     

An application of cokriging for estimation of tripartite earthquake response spectra

A tripartite earthquake response spectrum exhibits peak values of acceleration, velocity, and displacement in concert, each as a function of natural frequency of vibration. Because cokriging is a regionalized variable technique for multiple variable estimation, it was employed to jointly estimate peak values of acceleration, velocity, and displacement through a frequency discretization process. The objective of this application was to develop a technique for estimation of response spectra at uninstrumented locations. Because magnitudes of the three response variables differed, these data were normalized prior to cokriging. This process simply involved dividing each type of variable by its maximum value for a given frequency; hence, values of each type of variable ranged between zero and one. This allowed better accuracy in developing cross-variograms. Cokriging proved to be an efficient and accurate technique to use for the estimation of tripartite response spectra.     

协同克立格法在广西林旺金矿化探数据处理中的应用

协同克立格法,同时兼具化探数据多元性及克立格法表征空间属性的特点。考虑到地质变量两个以上的空间属性,在化探数据处理中运用协同克立格法,可以进一步提高估计精度。运用协同克立格法对广西林旺矿区中金元素成矿进行预测,经相关性分析显示,在矿区中元素的基本组合是Au、Ag、As、Hg,协同克立格插值以Au为主要变量,伴生元素Ag、As、Hg为次要变量。把插值计算后的结果与传统多元统计方法和普通克立格法的计算结果进行比较,结果协同克立格法得到的估值误差较小,预测精度较高,在成矿元素的预测中具有一定程度的优越性。     

Universal cokriging under intrinsic coregionalization

Under the intrinsic coregionalization model if both primary and secondary measurements are available at all sample locations, the conventional geostatistical wisdom is that cokriging provides exactly the same solution as univariate kriging on the primary process alone. However, recent eamples have been given where nonzero secondary cokriging weights have accurred under this spatial dependence structure. This note identifies the conditions under which secondary information is useful under the assumption of intrinsic coregionalization. An illustration is given using a dataset of plutonium and americium concentrations collected from a region of the Nevada Test Site.     

Bed sediment entrainment by streamflow: State of the science

In fluvial sedimentology, bed sediment entrainment by streamflow has a decisive role in controlling several fluvial processes. Owing to its huge practical importance, the subject has been painstakingly explored for over a century. However, a detailed understanding of the mechanism of the bed sediment entrainment phenomenon achieved hitherto is far from complete. The central theme of bed sediment entrainment is occupied by the sediment entrainment threshold, which varies enormously in its qualitative definition, identification and quantification encompassing a broad range of spatiotemporal scales. This article presents the state of the science of the entrainment of non‐cohesive bed sediments under a steady‐unidirectional streamflow. It begins with the diverse definitions and representations of the entrainment threshold criterion from both qualitative and quantitative perspectives, scrutinising its suitability and ambit of applicability. Then, the effects of energetic factors that drive the entrainment threshold criterion are critically appraised. The indispensable mechanisms of bed sediment entrainment, including the theoretical background and modelling strategies, the role of turbulent bursting phenomenon and the phenomenological perspective into the origin of the scaling laws of sediment entrainment, are explained. Throughout the article, special emphasis is given to the strengths and weaknesses of the current state of the science. In addition, a deliberate attempt is made to invoke the thought‐provoking ideas on the multifarious features of bed sediment entrainment. Finally, the innovative perspectives on the bed sediment entrainment are provided and the concluding remarks are made, elucidating the major challenges and suggesting the prospective ways to resolve them as a future scope of research.     

Successive Nonparametric Estimation of Conditional Distributions

Spatial characterization of non-Gaussian attributes in earth sciences and engineering commonly requires the estimation of their conditional distribution. The indicator and probability kriging approaches of current nonparametric geostatistics provide approximations for estimating conditional distributions. They do not, however, provide results similar to those in the cumbersome implementation of simultaneous cokriging of indicators. This paper presents a new formulation termed successive cokriging of indicators that avoids the classic simultaneous solution and related computational problems, while obtaining equivalent results to the impractical simultaneous solution of cokriging of indicators. A successive minimization of the estimation variance of probability estimates is performed, as additional data are successively included into the estimation process. In addition, the approach leads to an efficient nonparametric simulation algorithm for non-Gaussian random functions based on residual probabilities.     

利用树轮资料重建河流径流量研究进展

利用树轮资料重建河流径流量是树木年轮学研究的一个重要方向。在理解树轮水文学科学概念的基础上,介绍了利用树轮资料重建河流径流量的研究方法,综述了国际上利用树轮资料重建径流量的研究进展。从研究区域、思路与方法、应用领域等3个方面详细综述了中国利用树轮资料重建河流径流量的研究进展,概述了研究存在的问题及未来的展望。结论表明,利用树轮资料重建长尺度的径流序列,能更好地满足江河流域水资源统一管理和规划的需要,能为水资源管理提供丰富的基础资料。     

台湾多站流量生成模式的研究

在台湾不同时间下之流量均呈现强烈的气候特性,透过具有气候意义的流量模式,可使得模拟模式的结果更接近实际情况.利用台湾的气候特性,将流量区分于不同气候之贡献,初步完成具台湾气候特性的单站流量生成模式.再使用统计方法考虑于同一流域中不同时段与不同河川间之流量,最后形成合适的多站流量模式.经由多站流量生成模式所得之流量,不似单站生成模式缺乏流域整体的考虑,同时也保持河川间的相关性,与流量间时序之关系.将此模式应用在台湾淡水河流域的支流上,已获致颇佳的结果.此具气象性质之多站流量生成模式未来适合推广于台湾其它流域之水资源规划.     

天山北坡精河1615—2007年径流量变化的树轮记录

中国天山北坡西部精河流域山区的树木年轮记录了气候与水文变化过程,利用树轮宽度重建流域径流量长期变化历史对艾比湖湿地自然保护区生态保护和流域水资源利用具有重要意义.建立了精河流域山区2个采样点的天山云杉树轮宽度年表,分析其对流域气象和水文要素的响应特征,建立了树轮宽度标准年表与精河水文站上年9月到当年8月径流量的线性转换方程(R2=37.5%, P<0.001),重建了公元1615—2007年的径流量变化历史.丰枯年份和持续丰枯期分析表明:精河出山口径流量重建序列包含7个丰水年和11个枯水年,且发生了13次持续丰水期和10次持续枯水期.多窗谱分析发现径流量序列在99%的置信水平上存在56.8 年、6.9 年、3.8 年、3.4 年、2.0~2.1 年周期,其中6.9 年对应厄尔尼诺-南方涛动(ENSO)事件的周期,同时还发现了重建序列与南方涛动指数的显著负相关(r =-0.329,n=56),表明研究区径流量受大尺度海气耦合模式的影响.精河径流量序列与天山北坡玛纳斯河和乌鲁木齐河的丰枯阶段以及天山山区、伊犁地区降水变化的干湿阶段较好的对应,表明天山北坡水文和气候变化的大尺度环流背景和驱动因子一致.     

Minimum-variance unbiased quadratic estimation of covariances of regionalized variables

The parameters of covariance functions (or variograms) of regionalized variables must be determined before linear unbiased estimation can be applied. This work examines the problem of minimum-variance unbiased quadratic estimation of the parameters of ordinary or generalized covariance functions of regionalized variables. Attention is limited to covariance functions that are linear in the parameters and the normality assumption is invoked when fourth moments of the data need to be calculated. The main contributions of this work are (1) it shows when and in what sense minimum-variance unbiased quadratic estimation can be achieved, and (2) it yields a well-founded, practicable, and easy-to-automate methodology for the estimation of parameters of covariance functions. Results of simulation studies are very encouraging.     

Identifying spatial heterogeneity of coal resource quality in a multilayer coal deposit by multivariate geostatistics

This study presents a new geostatistical approach to characterization of the geometry and quality of a multilayer coal deposit using the data of seam thickness as a geometric property and the contents of ash, sodium, total sulphur, and the heating value as quality properties. A coal deposit in East Kalimantan (Borneo), Indonesia, which has a synclinal geological structure, was chosen as the study site. Semivariogram analysis clarified the strong dependence of heating value on ash content in the top and bottom parts of each seam and the existence of a strong correlation with sodium content over the sub-seams in the same location. The correlations between the geometry and quality of the seams were generally weak. A linear coregionalization model was used to derive the spatial correlation coefficients of two variables at each scale component from the single- and cross-semivariogram matrices. Because the data were correlated spatially in the same seam or over different seams, multivariate techniques (ordinary cokriging and factorial cokriging) were mainly used and the resultant spatial estimates were compared to those derived using a univariate technique (ordinary kriging). A factorial cokriging was effective to decompose the spatial correlation structures with different scales. Another important characteristic was that the sodium content shows distinct segregation: the low zones are concentrated near the boundary of the sedimentary basin, while the high zones are concentrated in the central part. The main component of sodium originates from the abundance of saline water. Therefore, it can be inferred that seawater had stronger effects on the coal depositional process in the central basin than in the border part. The geostatistical modeling results suggest that the thicknesses of all the major seams were controlled by the syncline structure, while the coal qualities chiefly were originated from the coal depositional and diagenetic processes.     

Multidimensional spectrum estimation for nonstationary processes

A spectrum estimation method for multidimensional nonstationary processes has been developed. The estimation method has been applied to a nonstationary two-dimensional random field. The numerical findings show that the results of the estimations are about what can be expected from a multidimensional estimation for a nonstationary process.     

推求地面径流单位线的Free Search算法

地面径流单位线在水文计算和水文预报工作中应用十分普遍,但当净雨时段较多时,传统的单位线推求方法存在工作量大、效率不高、过分依赖专业经验、计算过程复杂、模拟结果可能出现负值等问题。为此,本文引入源于动物群体迁移行为的自由搜索(Free Search,FS)算法,将FS单个动物每步探查行走的位置向量作为一条初始单位线,在FS算法迭代过程中再将所有的初始单位线转化为符合定义的单位线,从而利用动物群体的迁移行为推求出最优单位线。该方法的优点是概念清晰,操作简便,能够直接给出单位线的各时段流量值。三个典型实例模拟结果表明:利用FS推求单位线时,寻优一次即可得到满意结果,所得单位线不需要修正,并且能够有效克服锯齿现象,对地面径流量的模拟精度也较高。     

Conditional simulation of intrinsic random functions of order k

Conditional simulation of intrinsic random functions of orderk is a stochastic method that generates realizations which mimic the spatial fluctuation of nonstationary phenomena, reproduce their generalized covariance and honor the available data at sampled locations. The technique proposed here requires the following steps: (i) on-line simulation of Wiener-Levy processes and of their integrations; (ii) use of the turning-bands method to generate realizations in Rⁿ; (iii) conditioning to available data; and (iv) verification of the reproduced generalized covariance using generalized variograms. The applicational aspects of the technique are demonstrated in two and three dimensions. Examples include the conditional simulation of geological variates of the Crystal Viking petroleum reservoir, Alberta, Canada.     

克立格估计的分析解释与协方差函数的代数确定

首先引入利用旋转面作为基函数的函数逼近概念, 在此基础上经过复杂的矩阵推导证明泛克立格法可表示为传统的带权最小二乘多项式拟合与以旋转面作为基函数的函数逼近, 并在一定条件下(随机场高度连续无块金效应) 论证了协方差(即旋转面) 的参数可通过数学分析的方法确定, 给出了以高斯函数为例确定协方差函数的两个准则.      

3D Property Modeling of Void Ratio by Cokriging

Void ratio measures compactness of ground soil in geotechnical engineering. When samples are collected in certain area for mapping void ratios, other relevant types of properties such as water content may be also analyzed. To map the spatial distribution of void ratio in the area based on these types of point, observation data interpolation is often needed. Owing to the variance of sampling density along the horizontal and vertical directions, special consideration is required to handle anisotropy of estimator. 3D property modeling aims at predicting the overall distribution of property values from limited samples, and geostatistical method can he employed naturally here because they help to minimize the mean square error of estimation. To construct 3D property model of void ratio, cokriging was used considering its mutual correlation with water content, which is another important soil parameter. Moreover, K-D tree was adopted to organize the samples to accelerate neighbor query in 3D space during the above modeling process. At last, spatial configuration of void ratio distribution in an engineering body was modeled through 3D visualization, which provides important information for civil engineering purpose.     

Generalized cross-validation for covariance model selection

A weighted cross-validation technique known in the spline literature as generalized cross-validation (GCV), is proposed for covariance model selection and parameter estimation. Weights for prediction errors are selected to give more importance to a cluster of points than isolated points. Clustered points are estimated better by their neighbors and are more sensitive to model parameters. This rational weighting scheme also provides a simplifying significantly the computation of the cross-validation mean square error of prediction. With small- to medium-size datasets, GCV is performed in a global neighborhood. Optimization of usual isotropic models requires only a small number of matrix inversions. A small dataset and a simulation are used to compare performances of GCV to ordinary cross-validation (OCV) and least-squares filling (LS).