Practical Incorporation of Multivariate Parameter Uncertainty in Geostatistical Resource Modeling

There is a need to bridge theory and practice for incorporating parameter uncertainty in geostatistical simulation modeling workflows. Simulation workflows are a standard practice in natural resource and recovery modeling, but the incorporation of multivariate parameter uncertainty into those workflows is challenging. However, the objectives can be met without considerable extra effort and programming. The sampling distributions of statistics comprise the core theoretical notion with the addition of the spatial degrees of freedom to account for the redundancy in the spatially correlated data. Prior parameter uncertainty is estimated from multivariate spatial resampling. Simulation-based transfer of prior parameter uncertainty results in posterior distributions which are updated by data conditioning and the model domain extents and configuration. The results are theoretically tractable and practical to achieve, providing realistic assessments of uncertainty by accounting for large-scale parameter uncertainty, which is often the most important component impacting a project. A simulation-based multivariate workflow demonstrates joint modeling of intrinsic shale properties and uncertainty in estimated ultimate recovery in a shale gas project. The multivariate workflow accounts for joint prior parameter uncertainty given the current well locations and results in posterior estimates on global distributions of all modeled properties. This is achieved by transferring the joint prior parameter uncertainty through conditional simulations.     

降雨的空间不均性对模拟产流量和产沙量不确定的影响

在传统的水文/水质模型中,降雨被认为是在空间上均匀分布并且对模型输出的不确定性不产生影响。本文的目的是评价由于降雨的空间分布不均匀性对模型输出-产流量和产沙量-不确定性的影响。本文选取卢氏流域为研究区域,使用SWAT模型和流域内24个雨量站的降雨作为模型的输入。基于降雨空间分布均匀的假定下,每次用一个雨量站的点雨量来作为流域的面平均降雨量,模拟的产流量和产沙量的不确定性来自于降水的不均匀性。模拟的产流量和产沙量的不确定性大于降雨的不确定性,结果表明,在运用水文/水质模型时,为了准确的模拟、预测产流量和产沙量必须掌握降雨的空间分布特性并将其应用于水文、水质模拟之中。     

Uncertainty and sensitivity analysis: tools for GIS-based model implementation

A novel procedure to analyse the uncertainty associated to the output of GIS-based models is presented. The procedure can handle models of any degree of complexity that accept any kind of input data. Two important aspects of spatial modelling are addressed: the propagation of uncertainty from model inputs and model parameters up to the model output (uncertainty analysis); and the assessment of the relative importance of the sources of uncertainty in the output uncertainty (sensitivity analysis). Two main applications are proposed. The procedure allows implementation of a GIS-based model whose output can reliably support the decision process with an optimized allocation of resources for spatial data acquisition. This is possible in low cost strategy, based on numerical simulations on a small prototype of the GIS-based model. Furthermore, the procedure provides an effective model building tool to choose, from a group of alternative models, the best one in terms of cost-benefit analysis. A comprehensive case study is described. It concerns the implementation of a new GIS-based hydrologic model, whose goal is providing near real-time flood forecasting.     

Uncertainty propagation in wildland fire behaviour modelling

Rothermel's model is the most widely used fire behaviour model in wildland fire research and management. It is a complex model that considers 17 input variables describing fuel type, fuel moisture, terrain and wind. Uncertainties in the input variables can have a substantial impact on the resulting errors and have to be considered, especially when the results are used in spatial decision making. In this paper it is shown that the analysis of uncertainty propagation can be carried out with the Taylor series method. This method is computationally cheaper than Monte Carlo and offers easy-to-use, preliminary sensitivity estimations.     

降雨信息空间插值的不确定性分析

文章以潮白河流域为样区,根据58个雨量站1990年的降雨观测数据,采用反距离权重法、克立格法、样条函数法、趋势面法等插值方法,分析了站点数量变化、时间尺度变化、栅格像元的尺度变化、插值方法的差异对降雨数据空间插值结果的影响,剖析降雨插值中的不确定性。结果表明：（1）插值站点数量越大,区域降雨插值的不确定性越小;（2）像元尺度在50m~1000m间变化对降雨插值的不确定性只有微弱的影响;（3）对应于时间尺度由年到月到日的变化,降雨插值的不确定性随时间尺度的减小而显著增大;（4）不同插值方法影响到降雨空间插值的不确定性水平。为了减少降雨信息空间插值的不确定性,根本途径是要引入第三方相关变量,并将其整合到现有的插值算法中。高相关性变量的选取及其与插值模型的整合方式将成为降雨插值研究的主导方向。     

Uncertainty modeling and analysis of surface area calculation based on a regular grid digital elevation model (DEM)

In the field of digital terrain analysis (DTA), the principle and method of uncertainty in surface area calculation (SAC) have not been deeply developed and need to be further studied. This paper considers the uncertainty of data sources from the digital elevation model (DEM) and SAC in DTA to perform the following investigations: (a) truncation error (TE) modeling and analysis, (b) modeling and analysis of SAC propagation error (PE) by using Monte-Carlo simulation techniques and spatial autocorrelation error to simulate DEM uncertainty. The simulation experiments show that (a) without the introduction of the DEM error, higher DEM resolution and lower terrain complexity lead to smaller TE and absolute error (AE); (b) with the introduction of the DEM error, the DEM resolution and terrain complexity influence the AE and standard deviation (SD) of the SAC, but the trends by which the two values change may be not consistent; and (c) the spatial distribution of the introduced random error determines the size and degree of the deviation between the calculated result and the true value of the surface area. This study provides insights regarding the principle and method of uncertainty in SACs in geographic information science (GIScience) and provides guidance to quantify SAC uncertainty.     

空间数据关联规则挖掘的不确定性处理及度量

针对传统空间数据关联规则挖掘缺乏不确定性处理及度量的局限性,将空间数据的不确定性和空间数据挖掘的不确定性有机结合,初步建立了空间数据关联规则挖掘的不确定性处理模型及度量指标,包括空间数据不确定性的Monte Carlo模拟、基于不确定性空间数据的空间自相关度量和关联规则不确定性度量等,并以我国某地区环境调查数据为例进行验证。     

Uncertainty due to DEM error in landslide susceptibility mapping

Terrain attributes such as slope gradient and slope shape, computed from a gridded digital elevation model (DEM), are important input data for landslide susceptibility mapping. Errors in DEM can cause uncertainty in terrain attributes and thus influence landslide susceptibility mapping. Monte Carlo simulations have been used in this article to compare uncertainties due to DEM error in two representative landslide susceptibility mapping approaches: a recently developed expert knowledge and fuzzy logic-based approach to landslide susceptibility mapping (efLandslides), and a logistic regression approach that is representative of multivariate statistical approaches to landslide susceptibility mapping. The study area is located in the middle and upper reaches of the Yangtze River, China, and includes two adjacent areas with similar environmental conditions – one for efLandslides model development (approximately 250 km²) and the other for model extrapolation (approximately 4600 km²). Sequential Gaussian simulation was used to simulate DEM error fields at 25-m resolution with different magnitudes and spatial autocorrelation levels. Nine sets of simulations were generated. Each set included 100 realizations derived from a DEM error field specified by possible combinations of three standard deviation values (1, 7.5, and 15 m) for error magnitude and three range values (0, 60, and 120 m) for spatial autocorrelation. The overall uncertainties of both efLandslides and the logistic regression approach attributable to each model-simulated DEM error were evaluated based on a map of standard deviations of landslide susceptibility realizations. The uncertainty assessment showed that the overall uncertainty in efLandslides was less sensitive to DEM error than that in the logistic regression approach and that the overall uncertainties in both efLandslides and the logistic regression approach for the model-extrapolation area were generally lower than in the model-development area used in this study. Boxplots were produced by associating an independent validation set of 205 observed landslides in the model-extrapolation area with the resulting landslide susceptibility realizations. These boxplots showed that for all simulations, efLandslides produced more reasonable results than logistic regression.     

新安江模型参数的不确定性分析

水文模型的不确定性研究是水文科学研究的重要课题。模型参数的不确定性分析是水文模型不确定性研究的重要内容之一。本文采用GLUE方法分析新安江模型参数的不确定性,结论基于对不同水文特征流域的长时间径流模拟,研究发现大量"等效性"参数组存在。据此将参数总结为三类:第一类为非敏感参数,如上层张力水容量UM等。它们对似然判据,及确定性系数(R²)影响小。第二类为敏感性参数,如河网蓄水消退系数CS等,其特点是对R²的影响大。第三类为区域性敏感参数,如张力水蓄水容量曲线的方次B等,它们对R²的影响力跟流域特征密切相关。这些结论有助于理解新安江模型参数,为今后流域水文模拟提供参考。文中还展望了未来水文模型不确定性研究的发展方向。     

大尺度水循环模拟系统不确定性研究进展

水循环过程受众多自然因素和人为因素影响,决定了水循环系统的变化性和复杂性。水循环系统模型作为研究流域水文循环过程及演变规律的重要工具,必然也存在较大的不确定性,特别是对于大尺度陆-气耦合下的水循环模拟系统,其不确定性来源包括输入和参数不确定性、结构不确定性、方法不确定性以及初始和边界条件不确定性。本文在分析不确定性量化方法和传统水文模型不确定性研究基础上,重点评述当前大尺度水循环系统模拟的不确定性研究进展和存在的瓶颈问题,并介绍一种针对大型复杂动力系统的不确定性量化解决方案和工具系统-PSUADE,基于此讨论PSUADE在大尺度水循环模拟系统不确定性量化过程中的优势。     

Multiple Point Metrics to Assess Categorical Variable Models

Geostatistical models should be checked to ensure consistency with conditioning data and statistical inputs. These are minimum acceptance criteria. Often the first and second-order statistics such as the histogram and variogram of simulated geological realizations are compared to the input parameters to check the reasonableness of the simulation implementation. Assessing the reproduction of statistics beyond second-order is often not considered because the “correct” higher order statistics are rarely known. With multiple point simulation (MPS) geostatistical methods, practitioners are now explicitly modeling higher-order statistics taken from a training image (TI). This article explores methods for extending minimum acceptance criteria to multiple point statistical comparisons between geostatistical realizations made with MPS algorithms and the associated TI. The intent is to assess how well the geostatistical models have reproduced the input statistics of the TI; akin to assessing the histogram and variogram reproduction in traditional semivariogram-based geostatistics. A number of metrics are presented to compare the input multiple point statistics of the TI with the statistics of the geostatistical realizations. These metrics are (1) first and second-order statistics, (2) trends, (3) the multiscale histogram, (4) the multiple point density function, and (5) the missing bins in the multiple point density function. A case study using MPS realizations is presented to demonstrate the proposed metrics; however, the metrics are not limited to specific MPS realizations. Comparisons could be made between any reference numerical analogue model and any simulated categorical variable model.     

Combining spatial transition probabilities for stochastic simulation of categorical fields

Categorical spatial data, such as land use classes and socioeconomic statistics data, are important data sources in geographical information science (GIS). The investigation of spatial patterns implied in these data can benefit many aspects of GIS research, such as classification of spatial data, spatial data mining, and spatial uncertainty modeling. However, the discrete nature of categorical data limits the application of traditional kriging methods widely used in Gaussian random fields. In this article, we present a new probabilistic method for modeling the posterior probability of class occurrence at any target location in space-given known class labels at source data locations within a neighborhood around that prediction location. In the proposed method, transition probabilities rather than indicator covariances or variograms are used as measures of spatial structure and the conditional or posterior (multi-point) probability is approximated by a weighted combination of preposterior (two-point) transition probabilities, while accounting for spatial interdependencies often ignored by existing approaches. In addition, the connections of the proposed method with probabilistic graphical models (Bayesian networks) and weights of evidence method are also discussed. The advantages of this new proposed approach are analyzed and highlighted through a case study involving the generation of spatial patterns via sequential indicator simulation.     

A Bootstrap Approach to Computing Uncertainty in Inferred Oil and Gas Reserve Estimates

This study develops confidence intervals for estimates of inferred oil and gas reserves based on bootstrap procedures. Inferred reserves are expected additions to proved reserves in previously discovered conventional oil and gas fields. Estimates of inferred reserves accounted for 65% of the total oil and 34% of the total gas assessed in the U.S. Geological Survey's 1995 National Assessment of oil and gas in US onshore and State offshore areas. When the same computational methods used in the 1995 Assessment are applied to more recent data, the 80-year (from 1997 through 2076) inferred reserve estimates for pre-1997 discoveries located in the lower 48 onshore and state offshore areas amounted to a total of 39.7 billion barrels of oil (BBO) and 293 trillion cubic feet (TCF) of gas. The 90% confidence interval about the oil estimate derived from the bootstrap approach is 22.4 BBO to 69.5 BBO. The comparable 90% confidence interval for the inferred gas reserve estimate is 217 TCF to 413 TCF. The 90% confidence interval describes the uncertainty that should be attached to the estimates. It also provides a basis for developing scenarios to explore the implications for energy policy analysis.     

高时空分辨率FFCO2排放清单的构建方法及研究展望

化石能源（FF）CO₂排放是全球人为温室气体排放的主体,作为衔接国家排放清单和大气反演验证途径的关键环节,2019年联合国政府间气候变化专门委员会（IPCC）对《国家温室气体清单指南》进行修订,势必将推动高分辨率FFCO₂排放清单的进一步规范发展。本文结合修订版指南中对于高分辨率排放清单的具体要求,从全球尺度、国家及以下尺度两个层面对高时空分辨率FFCO₂排放清单的构建方法进行梳理和归纳,并对其研究趋势进行展望。① IPCC方法学的进一步修订与完善,将有助于进一步提高FFCO₂排放清单的时空分辨率和精度;而构建包含间接排放的高分辨率FFCO₂排放清单正在兴起。② 作为大气反演模型的先验数据,采用自下而上的部门方法,直接获取排放统计数据,是编制高分辨率FFCO₂排放清单的首要途径;而通过替代变量及建模途径进行排放总量的时空分配,也是编制高分辨率FFCO₂排放清单的必要手段。③ 清单的不确定性分析中,需要考虑时空分配所带来的不确定性信息;基于大气观测的反演验证途径将作为独立于排放清单的一种客观核算手段,将在清单的质量保证/质量控制与验证中发挥重要作用。     

An Alternative Classification Scheme for Uncertain Attribute Mapping

The reality of uncertain data cannot be ignored. Anytime that spatial data are used to assist planning, decision making, or policy generation, it is likely that error or uncertainty in the data will propagate through processing protocols and analytic techniques, potentially leading to biased or incorrect decision making. The ability to directly account for uncertainty in spatial analysis efforts is critically important. This article focuses on addressing data uncertainty in one of the most important and widely used exploratory spatial data analysis (ESDA) techniques—choropleth mapping—and proposes an alternative map classification method for uncertain spatial data. The classification approach maximizes within-class homogeneity under data uncertainty while explicitly integrating spatial characteristics to reduce visual map complexity and to facilitate pattern perception. The method is demonstrated by mapping the 2009 to 2013 American Community Survey estimates of median household income in Salt Lake County, Utah, at the census tract level.     

Multiple-Point Statistics for Training Image Selection

Selecting a training image (TI) that is representative of the target spatial phenomenon (reservoir, mineral deposit, soil type, etc.) is essential for an effective application of multiple-point statistics (MPS) simulation. It is often possible to narrow potential TIs to a general subset based on the available geological knowledge; however, this is largely subjective. A method is presented that compares the distribution of runs and the multiple-point density function from available exploration data and TIs. The difference in the MPS can be used to select the TI that is most representative of the data set. This tool may be applied to further narrow a suite of TIs for a more realistic model of spatial uncertainty. In addition, significant differences between the spatial statistics of local conditioning data and a TI may lead to artifacts in MPS. The utilization of this tool will identify contradictions between conditioning data and TIs. TI selection is demonstrated for a deepwater reservoir with 32 wells.     

基于场所的GIS中的不确定性问题及分类框架

基于场所的GIS直接表达人类地理空间知识的管理和加工过程,而不确定性是人类智能的基本特点,因此GIS的智能化需要研究其中的不确定性问题。与传统的GIS相比,基于场所的GIS中的不确定性问题更为丰富,既包括随机性,也包括含糊性,而不确定性的主体既可以是地理要素、场所和空间关系,也包括命题和规则。该文介绍该领域相关的研究成果,基于不确定性主体、类型、表达手段及相关的活动4个视角,建立了基于场所的GIS中所涉及的不确定性框架,从而为相关的不确定性建模提供指导。     

DEM误差对滑坡危险性评价模型的影响

基于数字高程模型(DEM)计算得到的坡度、坡向等地形属性是滑坡危险性评价模型的重要输入数据, DEM误差会导致地形属性计算结果不确定性, 进而影响滑坡危险性评价模型的结果。本文选择基于专家知识的滑坡危险性评价模型和逻辑斯第回归模型, 采用蒙特卡洛模拟方法, 研究DEM误差所导致的滑坡危险性评价模型结果不确定性。研究区位于长江中上游的重庆开县, 采用5 m分辨率的DEM, 以序贯高斯模拟方法模拟了不同大小(误差标准差为1 m、7.5 m、15 m)和空间自相关性(变程为0 m、30 m、60 m、120 m)的12 类DEM误差场参与滑坡危险性评价。每次模拟包括100 个实现, 通过对每次模拟分别计算滑坡危险性评价结果的标准差图层和分类一致性百分比图层, 用以评价结果不确定性。评价结果表明, 在不同的DEM精度下, 两个滑坡危险性评价模型所得结果的总体不确定性随空间自相关程度的变化趋势并不相同。当DEM空间自相关性程度不同时, 基于专家知识的滑坡危险性评价模型的评价结果总体不确定随着DEM误差增加而呈现不同的变化趋势, 而逻辑斯第回归模型的评价结果总体不确定性随着DEM误差大小增加而单调增加。从评价结果总体不确定性角度而言, 总体上逻辑斯第回归模型比基于专家知识的滑坡危险性评价模型更加依赖于DEM数据质量。     

Multicriteria generalization (MCG): a decision-making framework for formalizing multiscale environmental data reduction

Environmental simulation models need automated geographic data reduction methods to optimize the use of high-resolution data in complex environmental models. Advanced map generalization methods have been developed for multiscale geographic data representation. In the case of map generalization, positional, geometric and topological constraints are focused on to improve map legibility and communication of geographic semantics. In the context of environmental modelling, in addition to the spatial criteria, domain criteria and constraints also need to be considered. Currently, due to the absence of domain-specific generalization methods, modellers resort to ad hoc methods of manual digitization or use cartographic methods available in off-the-shelf software. Such manual methods are not feasible solutions when large data sets are to be processed, thus limiting modellers to the single-scale representations. Automated map generalization methods can rarely be used with confidence because simplified data sets may violate domain semantics and may also result in suboptimal model performance. For best modelling results, it is necessary to prioritize domain criteria and constraints during data generalization. Modellers should also be able to automate the generalization techniques and explore the trade-off between model efficiency and model simulation quality for alternative versions of input geographic data at different geographic scales. Based on our long-term research with experts in the analytic element method of groundwater modelling, we developed the multicriteria generalization (MCG) framework as a constraint-based approach to automated geographic data reduction. The MCG framework is based on the spatial multicriteria decision-making paradigm since multiscale data modelling is too complex to be fully automated and should be driven by modellers at each stage. Apart from a detailed discussion of the theoretical aspects of the MCG framework, we discuss two groundwater data modelling experiments that demonstrate how MCG is not just a framework for automated data reduction, but an approach for systematically exploring model performance at multiple geographic scales. Experimental results clearly indicate the benefits of MCG-based data reduction and encourage us to continue expanding the scope of and implement MCG for multiple application domains.     

A parallel computing approach to viewshed analysis of large terrain data using graphics processing units

Viewshed analysis, often supported by geographic information system, is widely used in many application domains. However, as terrain data continue to become increasingly large and available at high resolutions, data-intensive viewshed analysis poses significant computational challenges. General-purpose computation on graphics processing units (GPUs) provides a promising means to address such challenges. This article describes a parallel computing approach to data-intensive viewshed analysis of large terrain data using GPUs. Our approach exploits the high-bandwidth memory of GPUs and the parallelism of massive spatial data to enable memory-intensive and computation-intensive tasks while central processing units are used to achieve efficient input/output (I/O) management. Furthermore, a two-level spatial domain decomposition strategy has been developed to mitigate a performance bottleneck caused by data transfer in the memory hierarchy of GPU-based architecture. Computational experiments were designed to evaluate computational performance of the approach. The experiments demonstrate significant performance improvement over a well-known sequential computing method, and an enhanced ability of analyzing sizable datasets that the sequential computing method cannot handle.