Accounting for Parameter Uncertainty in Reservoir Uncertainty Assessment: The Conditional Finite-Domain Approach

An important aim of modern geostatistical modeling is to quantify uncertainty in geological systems. Geostatistical modeling requires many input parameters. The input univariate distribution or histogram is perhaps the most important. A new method for assessing uncertainty in the histogram, particularly uncertainty in the mean, is presented. This method, referred to as the conditional finite-domain (CFD) approach, accounts for the size of the domain and the local conditioning data. It is a stochastic approach based on a multivariate Gaussian distribution. The CFD approach is shown to be convergent, design independent, and parameterization invariant. The performance of the CFD approach is illustrated in a case study focusing on the impact of the number of data and the range of correlation on the limiting uncertainty in the parameters. The spatial bootstrap method and CFD approach are compared. As the number of data increases, uncertainty in the sample mean decreases in both the spatial bootstrap and the CFD. Contrary to spatial bootstrap, uncertainty in the sample mean in the CFD approach decreases as the range of correlation increases. This is a direct result of the conditioning data being more correlated to unsampled locations in the finite domain. The sensitivity of the limiting uncertainty relative to the variogram and the variable limits are also discussed.     

Ensemble adaptive tile prefetching using fuzzy logic

Prefetching is a process in which the necessary portion of data is predicted and loaded into memory beforehand. The increasing usage of geographic data in different types of applications has motivated the development of different prefetching techniques. Each prefetching technique serves a specific type of application, such as two-dimensional geographic information systems or three-dimensional visualization, and each one is crafted for the corresponding navigation patterns. However, as the boundary between these application types blurs, these techniques become insufficient for hybrid applications (such as digital moving maps), which embody various capabilities and navigation patterns. Therefore, a set of techniques should be used in combination to handle different prefetching requirements. In this study, a priority-based tile prefetching approach is proposed, which enables the ensemble usage of various techniques at the same time. The proposed approach manages these techniques dynamically through a fuzzy-logic-based inference engine to increase prefetching performance and to adapt to various exhibited behaviours. This engine performs adaptive decisions about the advantages of each technique according to their individual accuracy and activity level using fuzzy logic to determine how each prefetching technique performs. The results obtained from the experiments showed that up to a 25% increase in prefetching performance is achieved with the proposed ensemble usage over individual usage. A generic model for prefetching techniques was also developed and used to describe the given approach. Finally, a cross-platform software framework with four different prefetching techniques was developed to let other users utilize the proposed approach.     

Generic cumulative annular bucket histogram for spatial selectivity estimation of spatial database management system

Selectivity estimation is crucial to query optimizers in choosing an optimal execution plan in a given spatial query, and there has been a great deal of focus on how to achieve good selectivity estimation for finer spatial selection operators. Equally crucial to this is understanding how to produce an updated spatial histogram. With this in mind, we used a cumulative annular bucket histogram (AB histogram), which not only accurately estimates the selectivity of a spatial selection or a spatial join operation with finer operators but also provides an updated spatial histogram to estimate the selectivity of subsequent spatial operations in a multi-level spatial query plan. A basic unit of AB histogram stores the number of minimum bounding rectangles whose lower left points and upper right points are located in specific rectangular regions. According to the basic units of a cumulative AB histogram, we can find out the selectivity of a spatial selection with a number of different finer operators. When it comes to spatial join operations, a relationship between two cumulative AB histograms can be translated into a relationship between one histogram and numerous query windows from the other histogram. Furthermore, an updated cumulative AB histogram can be simultaneously built into the process of selectivity calculation, making it possible to achieve both selectivity and an updated histogram of spatial join; its implementation made in the optimizer facility (OPF) of INGRES9.2. To highlight the performance of a cumulative AB histogram, several experiments have been conducted, with results showing that the cumulative AB histogram not only supports the selectivity estimation of spatial selection and spatial join with ‘Disjoint’, ‘Intersect’, ‘Within’, ‘Contains’, ‘Crosses’ and ‘Overlap’ operators but also supports the generation of an updated histogram. This indicates that Ingres would do better to find a query plan with low-execution costs.     

Progressive vector compression for high-accuracy vector map data

With the increase in the number of applications using digital vector maps and the development of surveying techniques, a large volume of GIS (geographic information system) vector maps having high accuracy and precision is being produced. However, to achieve their effective transmission while preserving their high positional quality, these large amounts of vector map data need to be compressed. This paper presents a compression method based on a bin space partitioning data structure, which preserves a high-level accuracy and exact precision of spatial data. To achieve this, the proposed method a priori divides a map into rectangular local regions and classifies the bits of each object in the local regions to three types of bins, defined as category bin (CB), direction bin (DB), and accuracy bin (AB). Then, it encodes objects progressively using the properties of the classified bins, such as adjacency and orientation, to obtain the optimum compression ratio. Experimental results verify that our method can encode vector map data constituting less than 20% of the original map data at a 1-cm accuracy degree and that constituting less than 9% at a 1-m accuracy degree. In addition, its compression efficiency is greater than that of previous methods, whereas its complexity is lower for close to real-time applications.     

Estimating attendance from cellular network data

An automatic estimate of the number of attendees to events happening in the city can provide valuable information to geographic information systems and geo-located applications. We present a methodology to estimate the number of events’ attendees from cellular network data. In this work, we used anonymized Call Detail Records (CDRs) comprising data on where and when users access the cellular network. Our approach is based on two key ideas: (1) we identify the network cells associated with the event location. (2) We verify the attendance of each user, as a measure of whether (s)he generates CDRs during the event, but not during other times. We evaluate our approach to estimate the number of attendees to a number of events ranging from football matches in stadiums to concerts and festivals in open squares. Comparing our results with the best groundtruth data available, our estimates provide a median error of less than 15% of the actual number of attendees.     

Sequential Simulation Approach to Modeling of Multi-seam Coal Deposits with an Application to the Assessment of a Louisiana Lignite

There are multiple ways to characterize uncertainty in the assessment of coal resources, but not all of them are equally satisfactory. Increasingly, the tendency is toward borrowing from the statistical tools developed in the last 50 years for the quantitative assessment of other mineral commodities. Here, we briefly review the most recent of such methods and formulate a procedure for the systematic assessment of multi-seam coal deposits taking into account several geological factors, such as fluctuations in thickness, erosion, oxidation, and bed boundaries. A lignite deposit explored in three stages is used for validating models based on comparing a first set of drill holes against data from infill and development drilling. Results were fully consistent with reality, providing a variety of maps, histograms, and scatterplots characterizing the deposit and associated uncertainty in the assessments. The geostatistical approach was particularly informative in providing a probability distribution modeling deposit wide uncertainty about total resources and a cumulative distribution of coal tonnage as a function of local uncertainty.     

薄板光顺样条插值与中国气候空间模拟

利用720个气象台网的长期平均气象数据拟合具有三维地理空间的气候曲面,并与1km空间分辨率的数字高程模型相结合,对气候变量的规则栅格进行插值估计。对各月平均最低温度、平均最高温度和降水量的插值结果构成了基础数字气候空间,以满足地理信息系统的数据分析需求。插值过程提供的误差统计表明插值的温度误差普遍小于0.6度,降水误差范围在8%~15%,明显优于其它插值方法。样条法利用线性模型反映地形对气候的影响,并提供了简便的误差诊断程序,具有良好的实用性。     

Spatially constrained clustering of ecological units to facilitate the design of integrated water monitoring networks in the St. Lawrence Basin

Water monitoring networks are generally classified into surface water, precipitation, groundwater or water quality monitoring networks. The design of these networks typically occurs in isolation from each other. We present a regionalization approach to identify homogeneous subregions of large basins that are suitable as areas for the optimization of an integrated water monitoring network. The study area, which comprises a portion of the St. Lawrence Basin, was spatially divided using ecological units. For each ecological unit, 21 attributes were derived including both environmental and hydrological indicators. A spatially constrained regionalization technique was applied to define the final regions. A scree plot was used to determine the number of regions. The sensitivity of the technique to the correlation in the attribute data was removed by utilizing principal component analysis to reduce correlation between attribute data. During regionalization, the component values were weighted by their proportion of the total variance explained. The four regions in the final configuration had areas from 19% to 31% of the total area, 63,597 km². For the St. Lawrence Basin, this approach is effective for defining homogeneous regions that can be used in further research on the optimization of integrated water monitoring networks. The approach is portable to other regions and can incorporate any set of attribute data that is valuable to the regionalization objective.     

An inductive modelling procedure based on Bayes' theorem for analysis of pattern in spatial data

Abstract

This paper describes an inductive modelling procedure integrated with a geographical information system for analysis of pattern within spatial data. The aim of the modelling procedure is to predict the distribution within one data set by combining a number of other data sets. Data set combination is carried out using Bayes’ theorem. Inputs to the theorem, in the form of conditional probabilities, are derived from an inductive learning process in which attributes of the data set to be modelled are compared with attributes of a variety of predictor data sets. This process is carried out on random subsets of the data to generate error bounds on inputs for analysis of error propagation associated with the use of Bayes’ theorem to combine data sets in the GIS. The statistical significance of model inputs is calculated as part of the inductive learning process. Use of the modelling procedure is illustrated through the analysis of the winter habitat relationships of red deer in Grampian Region, north-east Scotland. The distribution of red deer in Deer Management Group areas in Gordon and in Kincardine and Deeside Districts is used to develop a model which predicts the distribution throughout Grampian Region; this is tested against red deer distribution in Moray District. Habitat data sets used for constructing the model are accumulated frost and altitude, obtained from maps, and land cover, derived from satellite imagery. Errors resulting from the use of Bayes’ theorem to combine data sets within the GIS and introduced in generalizing output from 50 m pixel to 1 km grid squares resolution are analysed and presented in a series of maps. This analysis of error trains is an integral part of the implemented analytical procedure and provides support to the interpretation of the results of modelling. Potential applications of the modelling procedure are discussed.     

美国俄亥俄州土壤有机碳密度空间分布(英文)

Historical database of National Soil Survey Center containing 1424 geo-referenced soil profiles was used in this study for estimating the organic carbon(SOC) for the soils of Ohio,USA.Specific objective of the study was to estimate the spatial distribution of SOC density(C stock per unit area) to 1.0-m depth for soils of Ohio using geographically weighted regression(GWR),and compare the results with that obtained from multiple linear regression(MLR).About 80% of the analytical data were used for calibration and 20% for validation.A total of 20 variables including terrain attributes,climate data,bedrock geology,and land use data were used for mapping the SOC density.Results showed that the GWR provided better estimations with the lowest(3.81 kg m 2) root mean square error(RMSE) than MLR approach.Total estimated SOC pool for soils in Ohio ranged from 727 to 742 Tg.This study demonstrates that,the local spatial statistical technique,the GWR can perform better in capturing the spatial distribution of SOC across the study region as compared to other global spatial statistical techniques such as MLR.Thus,GWR enhances the accuracy for mapping SOC density.     

On the spatial relationship between landslides and causative factors on Lantau Island, Hong Kong

This paper presents a statistical approach to study the spatial relationship between landslides and their causative factors at the regional level. The approach is based on digital databases, and incorporates such methods as statistics, spatial pattern analysis, and interactive mapping. Firstly, the authors propose an object-oriented conceptual model for describing a landslide event, and a combined database of landslides and environmental factors is constructed by integrating the various databases within such a conceptual framework. The statistical histogram, spatial overlay, and dynamic mapping methods are linked together to interactively evaluate the spatial pattern of the relationship between landslides and their causative factors. A case study of an extreme event in 1993 on Lantau Island indicates that rainfall intensity and the migration of the center of the rainstorm greatly influence the occurrence of landslides on Lantau Island. A regional difference in the relationship between landslides and topography is identified. Most of the landslides in the middle and western parts of the island occurred on slopes with slope angles of 25–35°, while in the eastern part, the corresponding range is 30–35°. Overlaying landslide data with land cover reveals that a large number of landslides occurred in the bareland and shrub-covered area, and in the transition zones between different vegetation types. The proposed approach can be used not only to analyze the general characteristics of such a relationship, but also to depict its spatial distribution and variation, thereby providing a sound basis for regional landslide prediction.     

Choosing Between Two Kind of Sampling Patterns Using Geostatistical Simulation: Regularly Spaced or at High Uncertainty Locations?

Data from a mineral deposit are commonly obtained by core drilling. This kind of sampling involves high costs, limiting the number of drill holes. Additional holes should be located to bring the maximum benefit. The benefit can be evaluated by various ways and must take into account the goals of sampling. This article presents a case study where the deposit has been sampled and the new drillings must be added to reduce the uncertainty about a transfer function, Net Present Value (NPV) of the mining project. There are basically two ways to choose locations where new drillings should be placed for cases where the aim of sampling is to reduce uncertainty about a global function: the addition of new drillings outlining a quasi regular grid with previously collected drillings or the addition of new drillings on the locations of high uncertainty about the attribute of interest (or the attribute that is considered most influential in the transfer function). The performances of these patterns on reducing the uncertainty measured by the function selected are compared. The results point out that the most efficient pattern relates to the distribution (histogram) of the uncertainty about the attribute of interest. Thus, the choice of which sampling pattern should be adopted varies depending on data distribution and its influence on the transfer function.     

遥感技术在湖泊环境变化研究中的应用和展望

遥感技术由于能够快速、宏观的获得研究区域的数据,已成为湖泊环境动态变化监测的重要技术手段。高分辨率的卫星遥感图像不仅可以为准确判读湖区地质地貌、自然与人为作用下的环境变化、盐湖矿产资源的分布等提供直观的影像,还能为湖泊水质监测、水深检测、水面温度反演以及盐湖卤水动态分析提供有价值的信息。遥感技术在湖泊环境变化研究中的应用正逐步从定性发展为定量研究,因此,对于区分湖泊水体中不同组分对遥感图像各光谱值的贡献等遥感机理的认识及理论尚需进一步深化,同时需要对处理遥感数据所运用的统计分析方法做进一步的改进以建立更加完善的遥感模型。今后,遥感技术和地理信息系统等多种信息处理工具的结合将是环境信息系统发展的主要方向。     

卫星数字图象处理与制图分析——以京津及邻区1:25万影象图的处理分析为例

利用计算机进行图象处理和彩色制印,编制了京津及邻区1:25万影象图。采用经数字处理的图象和制图分析等编改工艺,取得了高质量低成本的效果。     

Characterizing errors in digital elevation models and estimating the financial costs of accuracy

Digital topographic models are the foundation of more advanced modeling applications and ultimately inform planning and decision making in many fields. Despite this, the error associated with these models and derived attributes is commonly overlooked. Little attention has been given in the scientific literature to the benefits gained from having less error in a model or to the corresponding cost associated with reducing model error by choosing one product over another. To address these gaps in knowledge we evaluated the error associated with five digital elevation models (DEMs) and derived attributes of slope and aspect relative to the same attributes derived from LiDAR data. We also estimated the acquisition and processing costs per square kilometer of the five test models and the LiDAR models. We used three measures to characterize model error: (1) root mean square error, (2) mean error (and standard deviation), and (3) area of significant elevation error. We applied these measures to DEM products that are used extensively across a range of applications for planning and managing natural resources. We depicted the relationship between model accuracy (the inverse of error) and cost in two ways. One was accuracy/cost ratio for each model. The other used separate data on accuracy and cost to better guide potential users in choosing between models or deciding on necessary expenditure on models. The main conclusion of our work was that accounting for error in DEMs can inform choice of models and the need for financial outlays.     

A BOOTSTRAP RESAMPLING SCHEME FOR USING THE CANONICAL CORRELATION TECHNIQUE IN RANK ESTIMATION

Rank estimation by canonical correlation analysis in multivariate statistics has been proposed as analternative approach for estimating the number of components in a multicomponent mixture.Amethodological turning point of this new approach is that it focuses on the difference in structure ratherthan in magnitude in characterizing the difference between the signal and the noise.This structuraldifference is quantified through the analysis of canonical correlation,which is a well-established datareduction technique in multivariate statistics.Unfortunately,there is a price to be paid for having thisstructural difference:at least two replicate data matrices are needed to carry out the analysis.In this paper we continue to explore the potential and to extend the scope of the canonical correlationtechnique.In particular,we propose a bootstrap resampling method which makes it possible to performthe canonical correlation analysis on a single data matrix.Since a robust estimator is introduced to makeinference about the rank,the procedure may be applied to a wide range of data without any restrictionon the noise distribution.Results from real as well as simulated mixture samples indicate that when usedin conjunction with this resampling method,canonical correlation analysis of a single data matrix isequally efficient as of replicate data matrices.     

基于居住空间属性的人口数据空间化方法研究

精细尺度的人口分布是当前人口地理学研究的热点和难点,在灾害评估、资源配置、智慧城市建设等方面应用广泛。居住建筑物尺度作为精细尺度的重要内容,其人口数据空间化日益引起学术界的关注。本文以居住建筑斑块面积、斑块内建筑面积比重、建筑物层数、公摊率等居住空间属性为人口分布数量的指示因子,以居住建筑的轮廓斑块为人口分布位置的指示因子,利用街道界线和街道常住人口数据为控制单元,建立线性模型,获得了2015年宣城市宣州区6个街道的居住建筑物尺度的人口分布矢量数据,刻画了城市市区人口空间分布的细节信息。结果表明：①以居住空间属性作为人口空间分布的指示因子,获取的人口空间数据精度高,结果可信。29个社区(村)估算人数的相对误差绝对值的平均值低于7%,其中25个社区(村)的相对误差绝对值低于10%。在1102个居住建筑斑块中,估算人数在合理区内的斑块个数占比高于74%,轻微低估区(-10%, 0)和轻微高估区(0, 10%)的斑块总数占比高于9%;②由斑块面积和建筑物层数共同表征的建筑物体积,是建筑物尺度上影响人口空间分布的关键因素;斑块内建筑面积比重属性能进一步提高模型精度;公摊率属性具有“降高升低”作用,但将估算人数调节到合理区的“能力”较弱。     

Special Issue on parallel processing in GIS

This paper explores three theoretical approaches for estimating the degree of correctness to which the accuracy figures of a gridded Digital Elevation Model (DEM) have been estimated depending on the number of checkpoints involved in the assessment process. The widely used average‐error statistic Mean Square Error (MSE) was selected for measuring the DEM accuracy. The work was focused on DEM uncertainty assessment using approximate confidence intervals. Those confidence intervals were constructed both from classical methods which assume a normal distribution of the error and from a new method based on a non‐parametric approach. The first two approaches studied, called Chi‐squared and Asymptotic Student t, consider a normal distribution of the residuals. That is especially true in the first case. The second case, due to the asymptotic properties of the t distribution, can perform reasonably well with even slightly non‐normal residuals if the sample size is large enough. The third approach developed in this article is a new method based on the theory of estimating functions which could be considered much more general than the previous two cases. It is based on a non‐parametric approach where no particular distribution is assumed. Thus, we can avoid the strong assumption of distribution normality accepted in previous work and in the majority of current standards of positional accuracy. The three approaches were tested using Monte Carlo simulation for several populations of residuals generated from originally sampled data. Those original grid DEMs, considered as ground data, were collected by means of digital photogrammetric methods from seven areas displaying differing morphology employing a 2 by 2 m sampling interval. The original grid DEMs were subsampled to generate new lower‐resolution DEMs. Each of these new DEMs was then interpolated to retrieve its original resolution using two different procedures. Height differences between original and interpolated grid DEMs were calculated to obtain residual populations. One interpolation procedure resulted in slightly non‐normal residual populations, whereas the other produced very non‐normal residuals with frequent outliers. Monte Carlo simulations allow us to report that the estimating function approach was the most robust and general of those tested. In fact, the other two approaches, especially the Chi‐squared method, were clearly affected by the degree of normality of the residual population distribution, producing less reliable results than the estimating functions approach. This last method shows good results when applied to the different datasets, even in the case of more leptokurtic populations. In the worst cases, no more than 64–128 checkpoints were required to construct an estimate of the global error of the DEM with 95% confidence. The approach therefore is an important step towards saving time and money in the evaluation of DEM accuracy using a single average‐error statistic. Nevertheless, we must take into account that MSE is essentially a single global measure of deviations, and thus incapable of characterizing the spatial variations of errors over the interpolated surface.