Bayesian area-to-point kriging using expert knowledge as informative priors

Area-to-point (ATP) kriging is a common geostatistical framework to address the problem of spatial disaggregation or downscaling from block support observations (BSO) to point support (PoS) predictions for continuous variables. This approach requires that the PoS variogram is known. Without PoS observations, the parameters of the PoS variogram cannot be deterministically estimated from BSO, and as a result, the PoS variogram parameters are uncertain. In this research, we used Bayesian ATP conditional simulation to estimate the PoS variogram parameters from expert knowledge and BSO, and quantify uncertainty of the PoS variogram parameters and disaggregation outcomes. We first clarified that the nugget parameter of the PoS variogram cannot be estimated from only BSO. Next, we used statistical expert elicitation techniques to elicit the PoS variogram parameters from expert knowledge. These were used as informative priors in a Bayesian inference of the PoS variogram from BSO and implemented using a Markov chain Monte Carlo algorithm. ATP conditional simulation was done to obtain stochastic simulations at point support. MODIS (Moderate Resolution Imaging Spectroradiometer) atmospheric temperature profile data were used in an illustrative example. The outcomes from the Bayesian ATP inference for the Matérn variogram model parameters confirmed that the posterior distribution of the nugget parameter was effectively the same as its prior distribution; for the other parameters, the uncertainty was substantially decreased when BSO were introduced to the Bayesian ATP estimator. This confirmed that expert knowledge brought new information to infer the nugget effect at PoS while BSO only brought new information to infer the other parameters. Bayesian ATP conditional simulations provided a satisfactory way to quantify parameters and model uncertainty propagation through spatial disaggregation.     

Statistical data fusion of multi-sensor AOD over the Continental United States

This article illustrates two techniques for merging daily aerosol optical depth (AOD) measurements from satellite and ground-based data sources to achieve optimal data quality and spatial coverage. The first technique is a traditional Universal Kriging (UK) approach employed to predict AOD from multi-sensor aerosol products that are aggregated on a reference grid with AERONET as ground truth. The second technique is spatial statistical data fusion (SSDF); a method designed for massive satellite data interpolation. Traditional kriging has computational complexity O(N³), making it impractical for large datasets. Our version of UK accommodates massive data inputs by performing kriging locally, while SSDF accommodates massive data inputs by modelling their covariance structure with a low-rank linear model. In this study, we use aerosol data products from two satellite instruments: the moderate resolution imaging spectrometer and the geostationary operational environmental satellite, covering the Continental United States.     

Effect of growing watershed imperviousness on hydrograph parameters and peak discharge

An increasing impervious area is quickly extending over the Wu‐Tu watershed due to the endless demands of the people. Generally, impervious paving is a major result of urbanization and more recently has had the potential to produce more enormous flood disasters than those of the past. In this study, 40 available rainfall–runoff events were chosen to calibrate the applicable parameters of the models and to determine the relationships between the impervious surfaces and the calibrated parameters. Model inputs came from the outcomes of the block kriging method and the non‐linear programming method. In the optimal process, the shuffled complex evolution method and three criteria were applied to compare the observed and simulated hydrographs. The tendencies of the variations of the parameters with their corresponding imperviousness were established through regression analysis. Ten cases were used to examine the established equations of the parameters and impervious covers. Finally, the design flood routines of various return periods were furnished through use of approaches containing a design storm, block kriging, the SCS model, and a rainfall‐runoff model with established functional relationships. These simulated flood hydrographs were used to compare and understand the past, present, and future hydrological conditions of the watershed studied. In the research results, the time to peak of flood hydrographs for various storms was diminished approximately from 11 h to 6 h in different decrements, whereas peak flow increased respectively from 127 m³ s^?1 to 629 m³ s^?1 for different storm intensities. In addition, this study provides a design diagram for the peak flow ratio to help engineers and designers to construct hydraulic structures efficiently and prevent possible damage to human life and property. Copyright © 2007 John Wiley & Sons, Ltd.     

SOFTWARE REVIEWS

ATLAS*GIS , Version 1.0. ATLAS*MapMaker , Version 4.0. FIVFIV-SINSIN , Release 9.0. Geo-EAS , Version 1.2.1. Evan Englund Sim City , Version 1.0 Statistix , Version 3.1.     

UAVRS影像空中三角测量实验研究

无人飞行器低空遥感系统(UAV Low Altitude Remote Sensing System简称UAVRS系统)适合于在阴云山区低空获取高分辨率垂直和倾斜影像,但获取的影像存在像幅小、数量多、基线短、重叠度不规则且倾角过大等问题,而这些问题,都是国内外现有的数字摄影测量系统面临的新问题。本文提出以带权观测值光束法平差解决UAVRS复杂影像区域网的空中三角测量问题的方法。其技术要点在于,从提高单模型定向的精度出发,以单模型定向元素为基础构建自由区域网,为带权观测值光束法平差提供有效初值。经试验表明,空三加密点的平面精度为0.386m,高程精度为0.525m,基本能达到1∶2000地形图测图的要求。     

基于地球化学组合求异的津巴布韦奇马尼马尼地区成矿预测

如何有效地解释评价异常是化探找矿取得成功的关键,传统的地球化学异常处理方法一般是以单一元素的含量值与背景值的差异来圈定异常,因子-泛克立格求异模型则建立在矿床主成矿期元素共生组合与地球化学异常之间的对应关系。采用因子-泛克立格模型对津巴布韦东部奇马尼马尼地区进行成矿预测,结果表明:奇马尼马尼地区存在7种元素组合,分别对应于不同的岩性组合,F4和F6元素组合异常可作为区内热液成矿指示标志,与东部塔卡金矿套合程度高。利用该模型圈定了5处找矿远景区,Ⅰ号远景区为铜镍金钛铁矿成矿有利区,Ⅱ号远景区具有与塔卡金矿相似的地球化学组合背景,Ⅲ号、Ⅳ号和Ⅴ号远景区则具寻找热液型金铜矿及多金属矿的潜力。     

滑动窗口的普通克立格方法在降水量插值中的应用

利用2009年全国2200个观测站降水量资料,使用滑动窗口的普通克立格方法对降水量资料进行格点化估计。针对滑动窗口的普通克立格方法在降水量格点化应用中存在的问题,设计了3种技术处理的试验方案。比较了全局搜索与方位邻近方法的误差,讨论了最大影响半径及屏蔽效应对插值效果的作用。提出了方位邻近法的样本点选择策略,结果表明,相对传统滑动窗口的普通克立格方法较常使用的全局搜索法而言,方位邻近法显著降低了计算资源的耗用,同时又具有较高的插值精度,特别是在站点密集地区有突出的优势;试验结果也表明:变程为4°～5°的经(纬)线弧长时,在方位邻近法下,我国大部分区域有较好的插值效果;屏蔽效应弱,ε取值为0.1时,降水量插值准确率较高,随着ε增大,插值误差也逐渐增大。     

Geostatistical analysis and conditional simulation for estimating the spatial variability of hydraulic conductivity in the Choushui River alluvial fan,Taiwan

This work evaluated the spatial variability and distribution of heterogeneous hydraulic conductivity (K) in the Choushui River alluvial fan in Taiwan, using ordinary kriging (OK) and mean and individual sequential Gaussian simulations (SGS). A baseline flow model constructed by upscaling parameters was inversely calibrated to determine the pumping and recharge rates. Simulated heads using different K realizations were then compared with historically measured heads. A global/local simulated error between simulated and measured heads was analysed to assess the different spatial variabilities of various estimated K distributions. The results of a MODFLOW simulation indicate that the OK realization had the smallest sum of absolute mean simulation errors (SAMSE) and the SGS realizations preserved the spatial variability of the measured K fields. Moreover, the SAMSE increases as the spatial variability of the K field increases. The OK realization yields small local simulation errors in the measured K field of moderate magnitude, whereas the SGS realizations have small local simulation errors in the measured K fields, with high and low values. The OK realization of K can be applied to perform a deterministic inverse calibration. The mean SGS method is suggested for constructing a K field when the application focuses on extreme values of estimated parameters and small calibration errors, such as in a simulation of contaminant transport in heterogeneous aquifers. The individual SGS realization is useful in stochastically assessing the spatial uncertainty of highly heterogeneous aquifers. Copyright © 2004 John Wiley & Sons, Ltd.     

Comparison between different kriging estimators

Six different geostatistical estimators (linear kriging, lognormal kriging, and disjunctive kriging, each with and without a nonbias, i.e., universality condition) were compared using data from a polymetallic deposit in Algeria. The differences between estimators with and without the nonbias condition were far more pronounced than between the different kriging methods. This highlights the importance of choosing an appropriate stationarity model for the data. The criterion concerning kriging weight of the mean in simple kriging, proposed by Remacre (1984, 1987) and Rivoirard (1984) was found to be helpful for determining blocks where the choice of the stationarity hypothesis was critical.