Modelling soil map-unit inclusions by Monte Carlo simulation

Abstract

Error and uncertainty in spatial databases have gained considerable attention in recent years. The concern is that, as in other computer applications and, indeed, all analyses, poor quality input data will yield even worse output. Various methods for analysis of uncertainty have been developed, but none has been shown to be directly applicable to an actual geographical information system application in the area of natural resources. In spatial data on natural resources in general, and in soils data in particular, a major cause of error is the inclusion of unmapped units within areas delineated on the map as uniform. In this paper, two alternative algorithms for simulating inclusions in categorical natural resource maps are detailed. Their usefulness is shown by a simplified Monte Carlo testing to evaluate the accuracy of agricultural land valuation using land use and the soil information. Using two test areas it is possible to show that errors of as much as 6 per cent may result in the process of land valuation, with simulated valuations both above and below the actual values. Thus, although an actual monetary cost of the error term is estimated here, it is not found to be large.     

Modelling uncertainty in natural resource analysis using fuzzy sets and Monte Carlo simulation: slope stability prediction

The techniques of fuzzy logic and Monte Carlo simulation are combined to address two incompatible types of uncertainty present in most natural resource data: thematic classification uncertainty and variance in unclassified continuously distributed data. The resultant model of uncertainty is applied to an infinite slope stability model using data from Louise Island, British Columbia. Results are summarized so as to answer forestry decision support queries. The proposed model of uncertainty in resource data analysis is found to have utility in combining different types of uncertainty, and efficiently utilizing available metadata. Integration of uncertainty data models with visualization tools is considered a necessary prerequisite to effective implementation in decision support systems.     

Monte Carlo Simulations of Product Distributions and Contained Metal Estimates

Estimation of product distributions of two factors was simulated by conventional Monte Carlo techniques using factor distributions that were independent (uncorrelated). Several simulations using uniform distributions of factors show that the product distribution has a central peak approximately centered at the product of the medians of the factor distributions. Factor distributions that are peaked, such as Gaussian (normal) produce an even more peaked product distribution. Piecewise analytic solutions can be obtained for independent factor distributions and yield insight into the properties of the product distribution. As an example, porphyry copper grades and tonnages are now available in at least one public database and their distributions were analyzed. Although both grade and tonnage can be approximated with lognormal distributions, they are not exactly fit by them. The grade shows some nonlinear correlation with tonnage for the published database. Sampling by deposit from available databases of grade, tonnage, and geological details of each deposit specifies both grade and tonnage for that deposit. Any correlation between grade and tonnage is then preserved and the observed distribution of grades and tonnages can be used with no assumption of distribution form.     

Bayesian Analysis of the Discovery Process Model Using Markov Chain Monte Carlo

Based upon the Bayesian framework for analyzing the discovery sequence in a play, a Markov chain Monte Carlo sampler—the Metropolis–Hastings algorithm, is employed to sample model parameters and pool sizes from their joint posterior distribution. The proposed sampling scheme ensures that the parameter space of changing dimension can be traversed in spite of the unknown number of pools. The equal sample weights make it easy to obtain the confidence intervals and assess the statistical error in the estimates, so that the statistical behaviors of the discovery process modeling can be well understood. Two application examples of the Halten play in Norwegian Sea and the Bashaw reef play in the Western Canada Basin show that, the computational advantage of this method to the simple Monte Carlo integration is considerable. In order to increase the convergence speed of the sample chains to the posterior distributions, several parallel simulations with different starting values are recommended.     

基于蒙特卡罗方法的扎龙湿地水环境质量评价

为了简单有效地评价水质状况,建立了蒙特卡罗水质评价模型,对扎龙湿地北部(进水区)、中部(过水区)和南部(出水区)的污染状况进行评价,并与模糊综合评价结果、灰色关联评价结果和内梅罗评价结果进行比较.基于蒙特卡罗(Monte Carlo,MC)法的评价结果表明,扎龙湿地北部、中部和南部总体水质类别都为Ⅱ类,与模糊综合评价法和灰色关联评价法的评价结果一致,也与湿地水质的实际状况相吻合,从而证明了模型的准确性;而其与内梅罗指数法的评价结果差别较大,究其原因,内梅罗指数法评价结果表现为过保护,较严格,从而使得水质评价结果有些脱离实际,内梅罗指数法比较适于评价参评因子值波动比较小、各参评因子都污染较轻的研究区域.从单指标评价类别分析,溶解氧(DO)、Zn、Cd和Cu含量的评价类别一致;扎龙湿地北部和南部总磷(TP)含量的评价类别一致,中部和南部总氮(TN)含量评价类别一致;而Cr含量在3个区中的评价类别都不同,而且从北部、中部到南部逐渐增大,水质变差;另外由于南部地势较低,Cr在南部长期沉积和聚集也是导致其含量过高的重要原因之一.从各类别概率值之和分析,扎龙湿地内部各区隶属于Ⅱ类的概率值之和都是最大的,但隶属于劣Ⅴ类的概率值之和居第二,表明大部分区域水质较好,局部区域水质较差,考虑到水是流动的,水质有由好转差的风险;从北部到南部,隶属于Ⅰ类、Ⅲ类和劣Ⅴ类的概率值之和趋于减小,隶属于Ⅳ类的概率值之和基本未变,隶属于Ⅴ类的概率值之和稍有增加,水质趋于向Ⅱ类转化;从中部到南部,隶属于Ⅰ类、Ⅱ类和劣Ⅴ类的概率值之和减小,隶属于Ⅳ类的概率值之和基本未变,水质趋于向Ⅲ类和劣Ⅴ类水质转化.从平均值看,TP含量先减少后增大.扎龙湿地水质的评价结果表明,总体符合Ⅱ类水质及以上的概率约为54.5％,但个别指标评价结果不容乐观,尤其是Cd含量、DO含量和南部Cr含量的超标,应引起相关部门的注意.     

基于蒙特卡洛生存分析探究东北森林物候的影响因素

植被是生态环境变化的指示器,分析植被物候的影响因素不仅有助于气候变化分析,提高区域气候模式的模拟精度,而且对于准确评估植被生长趋势、生产力以及全球碳收支均具有重要意义。基于遥感的植物物候监测已取得了长足的发展和进步,但当前利用大范围、长时间序列的遥感数据分析植被物候影响因素的研究尚不多,采用线性回归模型对非线性的植被物候影响因素进行分析可能存在偏误。因此,本文提出一种基于蒙特卡洛模拟的生存分析方法,对东北森林物候的影响因素进行量化分析。首先利用东北森林地区1982-2009年间AVHRR GIMMS NDVI数据,应用双Logistic曲线拟合方法对植被春季返青期（SOS）、秋季落叶期（EOS）及植被生长期（GSL）进行提取;然后基于蒙特卡洛模拟和生存分析构建植被物候影响因素分析模型;最后运用所构建模型探讨了东北森林区春季返青期、秋季落叶期的可能影响因素。结果发现：温度、降水和风力对中国东北森林关键物候期有一定影响,其中温度是春季返青期和秋季落叶期的最主要驱动因素,长期平均温度比短期内的温度突变对物候影响更显著,落叶期前的风速增加有可能使落叶时间提前;除了环境因素,春季返青早的年间秋季落叶倾向于更晚。研究表明,结合蒙特卡洛方法的生存分析可以较好地对物候期的影响因素进行定量分析,可为物候现象的归因分析提供一种新的方法。     

Evaluating the uncertainty caused by Post Office Box addresses in environmental health studies: A restricted Monte Carlo approach

A Monte Carlo approach is used to evaluate the uncertainty caused by incorporating Post Office Box (PO Box) addresses in point‐cluster detection for an environmental‐health study. Placing PO Box addresses at the centroids of postcode polygons in conventional geocoding can introduce significant error into a cluster analysis of the point data generated from them. In the restricted Monte Carlo method I presented in this paper, an address that cannot be matched to a precise location is assigned a random location within the smallest polygon believed to contain that address. These random locations are then combined with the locations of precisely matched addresses, and the resulting dataset is used for performing cluster analysis. After repeating this randomization‐and‐analysis process many times, one can use the variance in the calculated cluster evaluation statistics to estimate the uncertainty caused by the addresses that cannot be precisely matched. This method maximizes the use of the available spatial information, while also providing a quantitative estimate of the uncertainty in that utilization. The method is applied to lung‐cancer data from Grafton County, New Hampshire, USA, in which the PO Box addresses account for more than half of the address dataset. The results show that less than 50% of the detected cluster area can be considered to have high certainty.     

Modelling the compliance of crustal rock—II. Response to temporal changes before earthquakes

There have been several claims that seismic shear waves respond to changes in stress before earthquakes. The companion paper develops a stress-sensitive model (APE) for the behaviour of low-porosity low-permeability crystalline rocks containing pervasive distributions of fluid-filled intergranular microcracks, and this paper uses APE to model the behaviour before earthquakes. Modelling with APE shows that the microgeometry and statistics of distributions of such fluid-filled microcracks respond almost immediately to changes in stress, and that the behaviour can be monitored by analysing seismic shear-wave splitting. The physical reasons for the coupling between shear-wave splitting and differential stress are discussed.
In this paper, we extend the model by using percolation theory to show that large crack densities are limited at the grain-scale level by the percolation threshold at which interacting crack clusters lead to pronounced increases in rock-matrix permeability. In the simplest formulation, the modelling is dimensionless and almost entirely constrained without free parameters. Nevertheless, APE modelling of the evolution of fluid-saturated rocks under stress reproduces the observed fracture criticality and the narrow range of shear-wave azimuthal anisotropy in crustal rocks. It also reproduces the behaviour of temporal variations in shear-wave splitting observed before and after the 1986, M = 6, North Palm Springs earthquake, Southern California, and several other smaller earthquakes.
The agreement of APE modelling with a wide range of observations confirms that fluid-saturated crystalline rocks are stress-sensitive and respond to changes in stress by critical fluid-rock interactions at the microscale level. This means that the effects of changes in stress and other parameters can be numerically modelled and monitored by appropriate observations of seismic shear waves.     

GIS-based stochastic modeling of physical accessibility using GPS-based floating car data and Monte Carlo simulation

The term physical accessibility has long been used by geographers, economists, and urban planners and reflects the relative ease of access to/from several urban/rural services by considering the traveling costs. Numerous accessibility measures, ranging from simple to sophisticated, can be observed in the geographical information systems (GIS)-based accessibility modeling literature. However, these measures are generally calculated from a constant catchment boundary (a most likely or average catchment boundary) based on constant deterministic transportation costs. This is one of the fundamental shortcomings of the current GIS-based accessibility modeling and creates uncertainty about the accuracy and reliability of the accessibility measures, especially when highly variable speeds in road segments are considered. The development of a new stochastic approach by using global positioning system (GPS)-based floating car data and Monte Carlo simulation (MCS) technique could enable handling the variations in transportation costs in a probabilistic manner and help to consider all possible catchment boundaries, instead of one average catchment boundary, in accessibility modeling process. Therefore, this article proposes a stochastic methodology for GIS-based accessibility modeling by using GPS-based floating car data and MCS technique. The proposed methodology is illustrated with a case study on medical emergency service accessibility in Eskisehir, Turkey. Moreover, deterministic and stochastic accessibility models are compared to demonstrate the differences between the models. The proposed model could provide better decision support for the decision-makers who are supposed to deal with accessibility, location/allocation, and service/catchment area related issues.