气象资料的统计降尺度方法综述

统计降尺度是解决由气象模式输出的低分辨率资料到流域尺度资料转换的手段之一,已成为一个重要的研究领域。统计降尺度方法十分丰富,分为传递函数法、天气形势法和天气发生器3类,3类之间并无严格的界限。统计降尺度涉及到时间与空间降尺度、随机型与确定型降尺度、时间自相关与空间相关性以及面向格点与面向站点的降尺度这4个方面的属性与分...     

Conditioning Simulations of Gaussian Random Fields by Ordinary Kriging

Conditioning realizations of stationary Gaussian random fields to a set of data is traditionally based on simple kriging. In practice, this approach may be demanding as it does not account for the uncertainty in the spatial average of the random field. In this paper, an alternative model is presented, in which the Gaussian field is decomposed into a random mean, constant over space but variable over the realizations, and an independent residual. It is shown that, when the prior variance of the random mean is infinitely large (reflecting prior ignorance on the actual spatial average), the realizations of the Gaussian random field are made conditional by substituting ordinary kriging for simple kriging. The proposed approach can be extended to models with random drifts that are polynomials in the spatial coordinates, by using universal or intrinsic kriging for conditioning the realizations, and also to multivariate situations by using cokriging instead of kriging.     

Learning soil parameters and updating geotechnical reliability estimates under spatial variability – theory and application to shallow foundations

ABSTRACT

Field data is commonly used to determine soil parameters for geotechnical analysis. Bayesian analysis allows combining field data with other information on soil parameters in a consistent manner. We show that the spatial variability of the soil properties and the associated measurements can be captured through two different modelling approaches. In the first approach, a single random variable (RV) represents the soil property within the area of interest, while the second approach models the spatial variability explicitly with a random field (RF). We apply the Bayesian concept exemplarily to the reliability assessment of a shallow foundation in a silty soil with spatially variable data. We show that the simpler RV approach is applicable in cases where the measurements do not influence the correlation structure of the soil property at the vicinity of the foundation. In other cases, it is expected to underestimate the reliability, and a RF model is required to obtain accurate results.     

数值天气预报检验方法研究进展

数值天气预报检验是改进及应用数值模式的重要环节。近年来,模式检验中的观念不断更新,适用于不同预报产品及不同用户需求的模式检验方法也不断涌现。首先简单回顾了以列联表为基础的传统的模式检验方法。其次重点总结了伴随高分辨率数值预报而出现的空间诊断检验技术,按照检验目的的不同,诊断方法可以归纳为:①基于滤波技术的分辨模式在不同时空尺度上预报能力的邻域法、尺度分离法;②利用位移偏差诊断模式预报位置、面积、方位、轴角等与观测差异的属性判别法、变形评估法。然后阐述了集合样本成员的概率分布函数(PDF)、集合预报与观测概率分布函数相似程度、事件发生的概率预报等集合预报检验方法。最后论述了空间诊断技术、集合预报检验方法的适用领域,并讨论了模式检验中存在的一些问题及未来的发展方向。     

Multivariate Spatial Modeling for Geostatistical Data Using Convolved Covariance Functions

Soil pollution data collection typically studies multivariate measurements at sampling locations, e.g., lead, zinc, copper or cadmium levels. With increased collection of such multivariate geostatistical spatial data, there arises the need for flexible explanatory stochastic models. Here, we propose a general constructive approach for building suitable models based upon convolution of covariance functions. We begin with a general theorem which asserts that, under weak conditions, cross convolution of covariance functions provides a valid cross covariance function. We also obtain a result on dependence induced by such convolution. Since, in general, convolution does not provide closed-form integration, we discuss efficient computation. We then suggest introducing such specification through a Gaussian process to model multivariate spatial random effects within a hierarchical model. We note that modeling spatial random effects in this way is parsimonious relative to say, the linear model of coregionalization. Through a limited simulation, we informally demonstrate that performance for these two specifications appears to be indistinguishable, encouraging the parsimonious choice. Finally, we use the convolved covariance model to analyze a trivariate pollution dataset from California.     

Isotropic Variogram Matrix Functions on Spheres

This paper is concerned with vector random fields on spheres with second-order increments, which are intrinsically stationary and mean square continuous and have isotropic variogram matrix functions. A characterization of the continuous and isotropic variogram matrix function on a sphere is derived, in terms of an infinite sum of the products of positive definite matrices and ultraspherical polynomials. It is valid for Gaussian or elliptically contoured vector random fields, but may not be valid for other non-Gaussian vector random fields on spheres such as a χ ², log-Gaussian, or skew-Gaussian vector random field. Some parametric variogram matrix models are derived on spheres via different constructional approaches. A simulation study is conducted to illustrate the implementation of the proposed model in estimation and cokriging, whose performance is compared with that using the linear model of coregionalization.     

The U-WEDGE Transformation Method for Multivariate Geostatistical Simulation

To speed up multivariate geostatistical simulation it is common to transform the set of attributes into spatially uncorrelated factors that can be simulated independently. Spatial decorrelation methods are usually based on the diagonalisation of the variance/covariance and semivariogram matrices of the set of attributes for a chosen family of lag spacings. These matrices are symmetric and there are several efficient methods for the approximate joint diagonalisation of a family of symmetric matrices. One of these is the uniformly weighted exhaustive diagonalisation with Gauss iterations (U-WEDGE) method. In contrast to the method of minimum/maximum autocorrelation factors (MAF), where a two structure linear model of coregionalisation is assumed, U-WEDGE can be applied directly to the set of experimental semivariogram matrices without having to place restrictions on the number of structures in the linear model of coregionalisation, thus removing one of the restrictions placed on the subsequent modelling of the spatial structure of the factors. We use an iron-ore data set to illustrate the method and present a comparison between the simulated attributes obtained from U-WEDGE and MAF with the full co-simulation of the attributes.     

Substitution Random Fields with Gaussian and Gamma Distributions: Theory and Application to a Pollution Data Set

This paper presents random field models with Gaussian or gamma univariate distributions and isofactorial bivariate distributions, constructed by composing two independent random fields: a directing function with stationary Gaussian increments and a stationary coding process with bivariate Gaussian or gamma distributions. Two variations are proposed, by considering a multivariate directing function and a coding process with a separable covariance, or by including drift components in the directing function. Iterative algorithms based on the Gibbs sampler allow one to condition the realizations of the substitution random fields to a set of data, while the inference of the model parameters relies on simple tools such as indicator variograms and variograms of different orders. A case study in polluted soil management is presented, for which a gamma model is used to quantify the risk that pollutant concentrations over remediation units exceed a given toxicity level. Unlike the multivariate Gaussian model, the proposed gamma model accounts for an asymmetry in the spatial correlation of the indicator functions around the median and for a spatial clustering of high pollutant concentrations.     

不排水抗剪强度非平稳随机场模拟及边坡可靠度分析

边坡可靠度分析中通常假定采用平稳或准平稳随机场表征土体参数的空间变异性,然而大量现场试验数据表明,土体参数如不排水抗剪强度沿土体埋深常呈现明显的非平稳分布特征,即其均值和标准差均随埋深发生变化,因此亟需发展土体参数非平稳随机场模型及其模拟方法。针对目前不能有效单独模拟土体参数趋势分量和随机波动分量的不确定性,提出了一种有效的不排水抗剪强度参数非平稳随机场模型,并给出了土体参数二维非平稳随机场模拟方法计算流程,同时将新提出的模型与现有非平稳随机场模型及平稳随机场模型进行了系统比较。最后通过不排水饱和黏土边坡算例验证了提出模型的有效性,并揭示了不排水抗剪强度非平稳分布特征对边坡可靠度的影响规律。结果表明：提出模型能够有效地单独模拟土体参数趋势分量和随机波动分量的不确定性,考虑土体参数均值和标准差随埋深增加而增大的特性,可为表征土体参数非平稳分布特征提供了一条有效的途径。此外,与采用非平稳随机场模拟土体参数空间变异性相比,采用常用的平稳随机场模型会低估边坡失效概率,从而造成偏危险的边坡工程设计方案。     

Bayesian Gaussian Mixture Linear Inversion for Geophysical Inverse Problems

A Bayesian linear inversion methodology based on Gaussian mixture models and its application to geophysical inverse problems are presented in this paper. The proposed inverse method is based on a Bayesian approach under the assumptions of a Gaussian mixture random field for the prior model and a Gaussian linear likelihood function. The model for the latent discrete variable is defined to be a stationary first-order Markov chain. In this approach, a recursive exact solution to an approximation of the posterior distribution of the inverse problem is proposed. A Markov chain Monte Carlo algorithm can be used to efficiently simulate realizations from the correct posterior model. Two inversion studies based on real well log data are presented, and the main results are the posterior distributions of the reservoir properties of interest, the corresponding predictions and prediction intervals, and a set of conditional realizations. The first application is a seismic inversion study for the prediction of lithological facies, P- and S-impedance, where an improvement of 30% in the root-mean-square error of the predictions compared to the traditional Gaussian inversion is obtained. The second application is a rock physics inversion study for the prediction of lithological facies, porosity, and clay volume, where predictions slightly improve compared to the Gaussian inversion approach.     

On the Use of Multivariate Lévy-Stable Random Field Models for Geological Heterogeneity

Increasing attention has been paid to the use of non-Gaussian distributions as models of heterogeneity in sedimentary formations in recent years. In particular, the Lévy-stable distribution has been shown to be a useful model of the distribution of the increments of data measured in well logs. Frequently, the width of this distribution follows a power–law type scaling with increment lag, thus suggesting a nonstationary, fractal, multivariate Lévy distribution as a useful random field model. However, in this paper we show that it is very difficult to formulate a multivariate Lévy distribution with any nontrivial spatial correlations that can be sampled from rigorously in large models. Conventional sequential simulation techniques require two properties to hold of a multivariate distribution in order to work: (1) the marginal distributions must be of relatively simple form, and (2) in the uncorrelated limit, the multivariate distribution must factor into a product of independent distributions. At least one of these properties will break down in a multivariate Lévy distribution, depending on how it is formulated. This makes a rigorous derivation of a sequential simulation algorithm impossible. Nonetheless, many of the original observations that spurred the original interest in multivariate Lévy distributions can be reproduced with a conventional normal scoring procedure. Secondly, an approximate formulation of a sequential simulation algorithm can adequately reproduce the Lévy distributions of increments and fractal scaling frequently seen in real data.     

Evaluation of geochemical data acquired from regular grids

Geochemical data obtained during mineral exploration often are biased by systematic as well as random errors; these may result in failures when usual methods of evaluation are used. This is true particularly in soil surveys carried out in regions where a long history of prospecting and mining activity has occurred and/or where aerial chemical pollution is likely to have occurred.A satisfactory evaluation of geochemical data even in such an unfavorable case requires sampling on a relatively dense grid and utilization of all available knowledge of types of mineralization. The evaluation procedure proposed consists of five consecutive phases: (1). Dividing the area of interest into subareas of a relatively homogeneous geological nature. (2). Processing by multivariate methods (factor analysis, in particular) without consideration of geographic relations. (3). A preliminary interpretation and search for a geochemical explanation of factors. (4). Processing of individual factors in two-dimensional geographic space by directional and frequency linear filtering methods. (5). Final interpretation and construction of a geochemical model. The procedure is illustrated by an example from a geochemical exploration survey in the vicinity of Píbram (Middle Bohemia).     

Optimization techniques for integrating spatial data

Two optimization techniques ta predict a spatial variable from any number of related spatial variables are presented. The applicability of the two different methods for petroleum-resource assessment is tested in a mature oil province of the Midcontinent (USA). The information on petroleum productivity, usually not directly accessible, is related indirectly to geological, geophysical, petrographical, and other observable data. This paper presents two approaches based on construction of a multivariate spatial model from the available data to determine a relationship for prediction. In the first approach, the variables are combined into a spatial model by an algebraic map-comparison/integration technique. Optimal weights for the map comparison function are determined by the Nelder-Mead downhill simplex algorithm in multidimensions. Geologic knowledge is necessary to provide a first guess of weights to start the automatization, because the solution is not unique. In the second approach, active set optimization for linear prediction of the target under positivity constraints is applied. Here, the procedure seems to select one variable from each data type (structure, isopachous, and petrophysical) eliminating data redundancy. Automating the determination of optimum combinations of different variables by applying optimization techniques is a valuable extension of the algebraic map-comparison/integration approach to analyzing spatial data. Because of the capability of handling multivariate data sets and partial retention of geographical information, the approaches can be useful in mineral-resource exploration.     

A particle tracking transport method for the simulation of resident and flux-averaged concentration of solute plumes in groundwater models

A new numerical technique called the convolution-based particle tracking (CBPT) method is developed to simulate resident or flux-averaged solute concentrations in groundwater models. The method is valid for steady-state flow and linear transport processes such as sorption with a linear sorption isotherm and first-order decay. The CBPT method uses particle tracking to take advantage of the ability of particle-based approaches to maintain sharp fronts for advection-dominated transport problems common in groundwater modeling and because of the flexibility of the random walk method to simulate a wide range of possible forms of the dispersion tensor. Furthermore, the algorithm for carrying out the convolution and superposition calculation from particle tracking results is very efficient. We show that from a single particle tracking run, source term variability, sorption, and decay can all be simulated rapidly without rerunning the underlying transport model unless the flow field or dispersion parameters are changed. A series of verification simulations are presented to demonstrate the accuracy and efficiency of the CBPT method compared to more conventional particle tracking approaches.     

Bayesian Spatial Prediction for Discrete Closed Skew Gaussian Random Field

Most approaches in statistical spatial prediction assume that the spatial data are realizations of a Gaussian random field. However, this assumption is hard to justify for most applications. When the distribution of data is skewed but otherwise has similar properties to the normal distribution, a closed skew normal distribution can be used for modeling their skewness. Closed skew normal distribution is an extension of the multivariate skew normal distribution and has the advantage of being closed under marginalization and conditioning. In this paper, we generalize Bayesian prediction methods using closed skew normal distributions. A simulation study is performed to check the validity of the model and performance of the Bayesian spatial predictor. Finally, our prediction method is applied to Bayesian spatial prediction on the strain data near Semnan, Iran. The mean-square error of cross-validation is improved by the closed skew Gaussian model on the strain data.     

The assessment of landslide susceptibility mapping using random forest and decision tree methods in the Three Gorges Reservoir area,China

Landslide susceptibility mapping is an indispensable prerequisite for landslide prevention and reduction. At present, research into landslide susceptibility mapping has begun to combine machine learning with remote sensing and geographic information system (GIS) techniques. The random forest model is a new integrated classification method, but its application to landslide susceptibility mapping remains limited. Landslides represent a serious threat to the lives and property of people living in the Zigui–Badong area in the Three Gorges region of China, as well as to the operation of the Three Gorges Reservoir. However, the geological structure of this region is complex, involving steep mountains and deep valleys. The purpose of the current study is to produce a landslide susceptibility map of the Zigui–Badong area using a random forest model, multisource data, GIS, and remote sensing data. In total, 300 pre-existing landslide locations were obtained from a landslide inventory map. These landslides were identified using visual interpretation of high-resolution remote sensing images, topographic and geologic data, and extensive field surveys. The occurrence of landslides is closely related to a series of environmental parameters. Topographic, geologic, Landsat-8 image, raining data, and seismic data were used as the primary data sources to extract the geo-environmental factors influencing landslides. Thirty-four layers of causative factors were prepared as predictor variables, which can mainly be categorized as topographic, geological, hydrological, land cover, and environmental trigger parameters. The random forest method is an ensemble classification technique that extends diversity among the classification trees by resampling the data with replacement and randomly changing the predictive variable sets during the different tree induction processes. A random forest model was adopted to calculate the quantitative relationships between the landslide-conditioning factors and the landslide inventory map and then generate a landslide susceptibility map. The analytical results were compared with known landslide locations in terms of area under the receiver operating characteristic curve. The random forest model has an area ratio of 86.10%. In contrast to the random forest (whole factors, WF), random forest (12 major factors, 12F), decision tree (WF), decision tree (12F), the final result shows that random forest (12F) has a higher prediction accuracy. Meanwhile, the random forest models have higher prediction accuracy than the decision tree model. Subsequently, the landslide susceptibility map was classified into five classes (very low, low, moderate, high, and very high). The results demonstrate that the random forest model achieved a reasonable accuracy in landslide susceptibility mapping. The landslide hazard zone information will be useful for general development planning and landslide risk management.     

Using the Entropy of Curves to Segment a Time or Spatial Series

The concept of the thermodynamics of curves is used to analyze change in the variability of time or spatial series. More specifically, the entropy of a curve makes it possible to divide a nonstationary random field, because of a change in variance, into subdomains where data are said to be stationary. It is demonstrated that for time and spatial series the entropy of a curve is the slope of the cumulative sum of absolute differences. Numerical simulations show the efficiency of this tool. It can be shown that the presence of a linear or quadratic trend is without effect on the localization of the stationary subdomains. A practical case is studied with data collected from a tunnel boring machine where several parameters are recorded. This analysis can bring more information on the mechanical behavior of the different geological formations and explain or justify unplanned delays.     

A Characterization of Symmetric Isofactorial Models

The paper examines symmetric isofactorial models. A necessary and sufficient condition for a bivariate stationary random function to be isofactorial is given. Using this characterization, a procedure for checking whether an isofactorial model is appropriate is outlined. If data indicates that an isofactorial model is adequate, the procedure also provides a method for identifying the factors of the model. The paper concentrates on the case where Z(x) takes values 0, 1, 2,..., N and the general case is discussed briefly.     

Comparative study on the equivalent linear and the fully nonlinear site response analysis approaches

Seismic site effect has been a major issue in the field of earthquake engineering due to the large local amplification of the seismic motion. This paper presents the importance of an appropriate soil behavior model to simulate earthquake site response and gives an overview of the field of site response analysis. Some of the well-known site response analysis methods are discussed. The objective of this paper is to investigate the influences of nonlinearity on the site response analysis by means of a more precise numerical model. In this respect, site responses of four different types of one-layered soil deposit, based on various shear wave velocities with the assumption of linear and rigid base bedrock, were analyzed by using the equivalent linear and fully nonlinear approaches. Nonlinear analyses?? results were compared with those of the linear method, and both of the similarities and differences are discussed. It is concluded that in the case of nonlinearity of soil under strong ground motions, 1-D equivalent linear modeling overestimates the amplification patterns in terms of absolute amplification level, and cannot correctly account for resonant frequencies and hysteric soil behavior. Therefore, more practical and appropriate numerical techniques for ground response analysis should be surveyed.