Probabilistic spatial prediction of categorical data using elliptical copulas

This study uses elliptical copulas and transition probabilities for uncertainty modeling of categorical spatial data. It begins by discussing the expressions of the cumulative distribution function and probability density function of two major elliptical copulas: Gaussian copula and t copula. The basic form of spatial copula discriminant function is then derived based on Bayes’ theorem, which consists of three parts: the prior probability, the conditional marginal densities, and the conditional copula density. Finally, three kinds of parameter estimation methods are discussed, including maximum likelihood estimation, inference functions for margins and canonical maximum likelihood (CML). To avoid making assumptions on the form of marginal distributions, the CML approach is adopted in the real-world case study. Results show that the occurrence probability maps generated by these two elliptical copulas are similar to each other. However, the prediction map interpolated by Gaussian copula has a relatively higher classification accuracy than t copula.     

Spatial prediction of categorical variables: the Bayesian maximum entropy approach

 Being a non-linear method based on a rigorous formalism and an efficient processing of various information sources, the Bayesian maximum entropy (BME) approach has proven to be a very powerful method in the context of continuous spatial random fields, providing much more satisfactory estimates than those obtained from traditional linear geostatistics (i.e., the various kriging techniques). This paper aims at presenting an extension of the BME formalism in the context of categorical spatial random fields. In the first part of the paper, the indicator kriging and cokriging methods are briefly presented and discussed. A special emphasis is put on their inherent limitations, both from the theoretical and practical point of view. The second part aims at presenting the theoretical developments of the BME approach for the case of categorical variables. The three-stage procedure is explained and the formulations for obtaining prior joint distributions and computing posterior conditional distributions are given for various typical cases. The last part of the paper consists in a simulation study for assessing the performance of BME over the traditional indicator (co)kriging techniques. The results of these simulations highlight the theoretical limitations of the indicator approach (negative probability estimates, probability distributions that do not sum up to one, etc.) as well as the much better performance of the BME approach. Estimates are very close to the theoretical conditional probabilities, that can be computed according to the stated simulation hypotheses.     

Bayesian data fusion in a spatial prediction context: a general formulation

In spite of the exponential growth in the amount of data that one may expect to provide greater modeling and predictions opportunities, the number and diversity of sources over which this information is fragmented is growing at an even faster rate. As a consequence, there is real need for methods that aim at reconciling them inside an epistemically sound theoretical framework. In a statistical spatial prediction framework, classical methods are based on a multivariate approach of the problem, at the price of strong modeling hypotheses. Though new avenues have been recently opened by focusing on the integration of uncertain data sources, to the best of our knowledges there have been no systematic attemps to explicitly account for information redundancy through a data fusion procedure. Starting from the simple concept of measurement errors, this paper proposes an approach for integrating multiple information processing as a part of the prediction process itself through a Bayesian approach. A general formulation is first proposed for deriving the prediction distribution of a continuous variable of interest at unsampled locations using on more or less uncertain (soft) information at neighboring locations. The case of multiple information is then considered, with a Bayesian solution to the problem of fusing multiple information that are provided as separate conditional probability distributions. Well-known methods and results are derived as limit cases. The convenient hypothesis of conditional independence is discussed by the light of information theory and maximum entropy principle, and a methodology is suggested for the optimal selection of the most informative subset of information, if needed. Based on a synthetic case study, an application of the methodology is presented and discussed.     

Approximate copula-based estimation and prediction of discrete spatial data

The present paper reports on the use of copula functions to describe the distribution of discrete spatial data, e.g. count data from environmental mapping or areal data analysis. In particular, we consider approaches to parameter point estimation and propose a fast method to perform approximate spatial prediction in copula-based spatial models with discrete marginal distributions. We assess the goodness of the resulting parameter estimates and predictors under different spatial settings and guide the analyst on which approach to apply for the data at hand. Finally, we illustrate the methodology by analyzing the well-known Lansing Woods data set. Software that implements the methods proposed in this paper is freely available in Matlab language on the author’s website.     

基于SVD分解的二维空间数据融合方法

建立地球全空间数据库需要研究空间数据融合的方法和智能技术.本文以布格重力异常数据的融合为例,介绍一种基于奇异值分解的二维空间数据融合方法.此方法在原理上可以实现融合后的数据集误差模不大于融合前的子数据集的最小误差模,相较于传统的融合处理方法原理更加先进.在算法中应用了权重矩阵,可使融合之后数据区域与原始数据的边界上梯度变化较小;运用有限差分法计算重力水平梯度,检验数据融合边界的效果.理论模型和实际数据试验表明,此方法可以保证数据隐含的重要属性完整保存,具有计算过程简单、适用范围广、融合效果好等特点,可以应用于位场等地球物理数据融合,也可以用于遥感和其他地理信息的数据融合.     

A universal kriging approach for spatial functional data

In a wide range of scientific fields the outputs coming from certain measurements often come in form of curves. In this paper we give a solution to the problem of spatial prediction of non-stationary functional data. We propose a new predictor by extending the classical universal kriging predictor for univariate data to the context of functional data. Using an approach similar to that used in univariate geostatistics we obtain a matrix system for estimating the weights of each functional variable on the prediction. The proposed methodology is validated by analyzing a real dataset corresponding to temperature curves obtained in several weather stations of Canada.     

A stochastic framework for downscaling processes of spatial averages based on the property of spectral multiscaling and its statistical diagnosis on spatio-temporal rainfall fields

Spectral multi-scaling postulates a power-law type of scaling of spectral distribution functions of stationary processes of spatial averages, over nested and geometrically similar sub-regions of the spatial parameter space of a given spatio-temporal random field. Presently a new framework is formulated for down-scaling processes of spatial averages, following naturally from the postulate of spectral multi-scaling, and key ingredients required for its implementation are described. Moreover, results from an extensive diagnostic study are presented, seeking statistical evidence supportive of spectral multi-scaling. Such evidence emerges from two sources of data. One is a 13 year long historical record of radar observations of rainfall in southeastern UK (Chenies radar), with high spatial (2 km) and temporal (5 min) resolution. The other is an ensemble of rain rate fields simulated by a spatio-temporal random pulse model fitted to the historical data. The results are consistent between historical and simulated rainfall data, indicating frequency-dependent scaling relationships interpreted as evidence of spectral multi-scaling across a range of spatial scales.     

Bootstrap approaches for spatial data

Generation of replicates of the available data enables the researchers to solve different statistical problems, such as the estimation of standard errors, the inference of parameters or even the approximation of distribution functions. With this aim, Bootstrap approaches are suggested in the current work, specifically designed for their application to spatial data, as they take into account the dependence structure of the underlying random process. The key idea is to construct nonparametric distribution estimators, adapted to the spatial setting, which are distribution functions themselves, associated to discrete or continuous random variables. Then, the Bootstrap samples are obtained by drawing at random from the estimated distribution. Consistency of the suggested approaches will be proved by assuming stationarity from the random process or by relaxing the latter hypothesis to admit a deterministic trend. Numerical studies for simulated data and a real data set, obtained from environmental monitoring, are included to illustrate the application of the proposed Bootstrap methods.     

OpenDA-NEMO framework for ocean data assimilation

Data assimilation methods provide a means to handle the modeling errors and uncertainties in sophisticated ocean models. In this study, we have created an OpenDA-NEMO framework unlocking the data assimilation tools available in OpenDA for use with NEMO models. This includes data assimilation methods, automatic parallelization, and a recently implemented automatic localization algorithm that removes spurious correlations in the model based on uncertainties in the computed Kalman gain matrix. We have set up a twin experiment where we assimilate sea surface height (SSH) satellite measurements. From the experiments, we can conclude that the OpenDA-NEMO framework performs as expected and that the automatic localization significantly improves the performance of the data assimilation algorithm by successfully removing spurious correlations. Based on these results, it looks promising to extend the framework with new kinds of observations and work on improving the computational speed of the automatic localization technique such that it becomes feasible to include large number of observations.     

A statistical estimator of the spatial distribution of the water-table altitude

An algorithm was designed to statistically estimate the areal distribution of water-table altitude. The altitude of the water table was bounded below by the minimum water-table surface and above by the land surface. Using lake elevations and stream stages, and interpolating between lakes and streams, the minimum water-table surface was generated. A multiple linear regression among the minimum water-table altitude, the differerence between land-surface and minimum water-table altitudes, and the water-level measurements from surficial aquifier system wells resulted in a consistently high correlation for all groups of physiographic regions in Florida. A simple linear regression between land-surface and water-level measurements resulted in a root-mean-square residual of 4.23 m, with residuals ranging from -8.78 to 41.54 m. A simple linear regression between the minimum water table and the water-level measurements resulted in a root-mean-square residual of 1.45 m, with residuals ranging from -7.39 to 4.10 m. The application of the multiple linear regression presented herein resulted in a root-mean-square residual of 1.05 m, with residuals ranging from -5.24 to 5.63 m. Results from complete and partial F tests rejected the hypothesis of eliminating any of the regressors in the multiple linear regression presented in this study.     

Techniques for statistical analysis and prediction of geophysical fluid systems

Abstract

Application of statistical estimators to analysis and prediction is examined from the point of view of geophysical fluid dynamics. The fundamental difficulty is that estimators constructed from observational records of limited length (the usual case in GFD) are sensitive to sampling errors in the statistics upon which they are based. To achieve meaningful results, the number of data, or input, parameters must be limited. The relationship between statistical and dynamical models (particularly clear for linear systems) coupled with certain statistical methods are explored with respect to the problem of input parameter selection, both for linear and nonlinear systems. Methods of assessing the effects of sampling errors in hindcasts are discussed and techniques for minimizing these effects in forecasts are evaluated. A method of efficiently condensing statistical models to a few input parameters and transfer functions is given. Finally the steps of hindcast analysis and forecaster construction are discussed from the practical point of view.     

An approximate method for joint sequential simulation of multiple spatial variables

Multivariate simulation is an important longstanding problem in geostatistics. Fitting a model of coregionalization to many variables is intractable and often not permitted; however, the matrix of collocated correlation coefficients is often well informed. Performing a matrix simulation with LU decomposition of the correlation matrix at each step of sequential simulation is implemented in some software. The target correlation matrix is not reproduced because of conditioning to local data and the particular variable ordering in the sequential/LU decomposition. A correction procedure is developed to calculate a modified correlation matrix that leads to reproduction of the target correlation matrix. The theoretical and practical aspects of this correction are developed.     

Test of statistical means for the extrapolation of soil depth point information using overlays of spatial environmental data and bootstrapping techniques

Hydrological modelling depends highly on the accuracy and uncertainty of model input parameters such as soil properties. Since most of these data are field surveyed, geostatistical techniques such as kriging, classification and regression trees or more sophisticated soil‐landscape models need to be applied to interpolate point information to the area. Most of the existing interpolation techniques require a random or regular distribution of points within the study area but are not adequate to satisfactorily interpolate soil catena or transect data. The soil landscape model presented in this study is predicting soil information from transect or catena point data using a statistical mean (arithmetic, geometric and harmonic mean) to calculate the soil information based on class means of merged spatial explanatory variables. A data set of 226 soil depth measurements covering a range of 0–6·5 m was used to test the model. The point data were sampled along four transects in the Stubbetorp catchment, SE‐Sweden. We overlaid a geomorphology map (8 classes) with digital elevation model‐derived topographic index maps (2–9 classes) to estimate the range of error the model produces with changing sample size and input maps. The accuracy of the soil depth predictions was estimated with the root mean square error (RMSE) based on a testing and training data set. RMSE ranged generally between 0·73 and 0·83 m ± 0·013 m depending on the amount of classes the merged layers had, but were smallest for a map combination with a low number of classes predicted with the harmonic mean (RMSE = 0·46 m). The results show that the prediction accuracy of this method depends on the number of point values in the sample, the value range of the measured attribute and the initial correlations between point values and explanatory variables, but suggests that the model approach is in general scale invariant. Copyright © 2009 John Wiley & Sons, Ltd.     

水库诱发地震震级预测的统计研究

于收集到的全球102例水库及已发地震的资料,应用隶属函数方法综合分析了水库基本属性、震中区岩性、库坝区基本烈度和震中区断层类型等与水库诱发地震之间的关系,从统计学角度给出了水库诱发最大地震震级的判定方法．通过回溯检验和费舍尔判别检验给出了预测震级的相对误差和正确识别率,总体预测效果较好,可为将来水库的设防和最大地震震级的判定提供统计学上的依据．      

一种适合多源地球物理数据三维可视化的快速空间索引技术

识别复杂地质条件下的地质构造,常需要融合多种地球物理探测技术的数据进行分析,应用地球物理数据三维可视化技术可以更好地解释复杂的地质现象,传统的可视化方法由于缺乏对多源地球物理数据一体化的存储管理与索引机制,使得在对大范围多源地球物理数据进行空间局部更加精细可视化时的效率很低.为了更有效地洞察研究区域的地下构造,本文研究了适合多源地球物理数据三维可视化技术的快速空间索引技术.首先根据各类地球物理数据空间分布特点,提出了一种改进的四叉树结构,用于建立对多源地球物理数据一体化存储与管理.接着利用该数据结构,文章现实了多源地球物理数据快速空间查询的机制.将此结构和机制服务于大规模多源地球物理数据精细尺度下的三维可视化,提高对特定空间范围的局部多源地球物理数据动态可视化的效率.最后给出了该数据结构下空间查询与可视化的效率分析,并通过实验对整个算法的效率进行了验证.实验表明,通过建立相应的索引机制,可在大规模多源地球物理数据条件下更高效地展示任意位置岩矿石多个物理特性之间的空间关系,为多源地球物理数据的三维可视化提供技术支撑.     

A data assimilation approach for groundwater parameter estimation under Bayesian maximum entropy framework

Spatial heterogeneity in groundwater system introduces significant challenges in groundwater modeling and parameter calibration. In order to mitigate the modeling uncertainty, data assiilation...     

A physics-based statistical algorithm for retrieving land surface temperature from AMSR-E passive microwave data

AMSR-E and MODIS are two EOS (Earth Observing System) instruments on board the Aqua satellite. A regression analysis between the brightness of all AMSR-E bands and the MODIS land surface tem-perature product indicated that the 89 GHz vertical polarization is the best single band to retrieve land surface temperature. According to simulation analysis with AIEM,the difference of different frequen-cies can eliminate the influence of water in soil and atmosphere,and also the surface roughness partly. The analysis results indicate that the radiation mechanism of surface covered snow is different from others. In order to retrieve land surface temperature more accurately,the land surface should be at least classified into three types:water covered surface,snow covered surface,and non-water and non-snow covered land surface. In order to improve the practicality and accuracy of the algorithm,we built different equations for different ranges of temperature. The average land surface temperature er-ror is about 2―3℃ relative to the MODIS LST product.     

Intelligent data fusion for wide-area assessment of UXO contamination

The remediation of sites contaminated with unexploded ordnance (UXO) remains an area of intense focus for the Department of Defense. Under the sponsorship of SERDP, data fusion techniques are being developed for use in enhancing wide-area assessment UXO remediation efforts and a data fusion framework is being created to provide a cohesive data management and decision-making utility to allow for more efficient expenditure of time, labor and resources. An important first step in this work is the development of feature extraction utilities and feature probability density maps for eventual input to data fusion algorithms, making data fusion of estimates of data quality, UXO-related features, non-UXO backgrounds, and correlations among independent data streams possible. Utilizing data acquired during ESTCP’s Wide-Area Assessment Pilot Program, the results presented here successfully demonstrate the feasibility of automated feature extraction from light detection and ranging, orthophotography, and helicopter magnetometry wide-area assessment survey data acquired at the Pueblo Precision Bombing Range #2. These data were imported and registered to a common survey map grid and UXO-related features were extracted and utilized to construct survey site-wide probability density maps that are well-suited for input to higher level data fusion algorithms. Preliminary combination of feature maps from the various data sources yielded maps for the Pueblo site that offered a more accurate UXO assessment than any one data source alone.