Improving copula-based spatial interpolation with secondary data
Improving copula-based spatial interpolation with secondary data
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DOI：
10.1016/j.spasta.2018.07.001
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发表时间：
2018-12-01
影响因子：
2.3
通讯作者：
Bardossy, Andras
中科院分区：
文献类型：
--
作者：
Gnann, Sebastian J.;Allmendinger, Max C.;Bardossy, Andras
通常情况下，所关注的主要变量只能很少地和/或间接地测量。因此，期望使用二次相关数据来改进对主要变量的估计。本文扩展了基于高斯Copula的地质统计插值方法，包括实值的主要和次要数据。此外，还纳入了多种实值二手数据和分类详尽二手信息，并分析了相关惠益。通过交叉验证和分裂抽样，将拟议纳入次级数据和信息的性能与基准地质统计方法（普通克里格法、协同克里格法、外部漂移克里格法和基于copula的主要变量插值法）进行了比较，主要变量和次级变量的组成各不相同。所提出的方法进行了测试，几个地下水质量参数和结果表明，a）联合copula为基础的方法优于协同克里格在所有质量措施;（B）物理上不可能的估计（即，（c）基于copula的方法在量化不确定性方面优于克里格方法，并导致更现实的不确定性空间格局。联合方法在主要变量在比次要变量更少的位置处可用的情况下导致更好的结果（即，当变量之间存在有意义的相关性时，在概率空间中构建的基于Copula的空间依赖模型中，防止了非正态（此处为双峰）边缘分布对联合分布和主要变量和次要变量的不同测量尺度的不利影响。该方法提供了一个有效的和非线性的替代co-Kriging。(C)2018爱思唯尔B. V.保留所有权利。
Often, the primary variable of interest can be measured only rarely and/or indirectly. Hence, it is desired to use secondary correlated data to improve the estimation of the primary variable. This paper extends the Gaussian copula-based geostatistical approach for interpolation to include both real-valued primary and secondary data. Even more, multiple types of real-valued secondary data and categorical exhaustive secondary information were incorporated and the associated benefits analysed. The performance of the proposed inclusion of secondary data and information was compared to benchmark geostatistical methods (Ordinary Kriging, coKriging, external drift Kriging, and copula-based interpolation of the primary variable alone) by cross-validation and split sampling, with varying compositions of primary and secondary variables. The proposed method was tested for several groundwater quality parameters and the results show that a) the joint copula-based method outperforms co-Kriging in all quality measures; (b) physically impossible estimates (i.e., negative concentrations) never occur; (c) copula-based methods outperform Kriging methods in the quantification of uncertainty and result in more realistic spatial patterns of uncertainty. Joint methods lead to better results in cases when the primary variable is available at fewer locations than the secondary variable (i.e., undersampled case) and when the variables are meaningfully related. In copula-based spatial dependence models that are constructed in probability space, detrimental effects of non-normal (here: bi-modal) marginal distributions on the joint distribution and dissimilar measurement scales of the primary and secondary variables are prevented. The proposed method offers an efficient and non-linear alternative to co-Kriging. (C) 2018 Elsevier B.V. All rights reserved.