Geostatistical interpolation using copulas
Geostatistical interpolation using copulas
复制标题
DOI：
10.1029/2007wr006115
复制
发表时间：
2008-07-24
影响因子：
5.4
通讯作者：
Li, Jing
中科院分区：
文献类型：
--
作者：
Bardossy, Andras;Li, Jing
在地质统计学方法的许多应用中，所研究的参数的相关结构仅用变差函数或协方差函数来描述，这容易受到测量异常的影响，并暗示高斯相关的假设。此外，克里金方差只考虑观测密度、数据几何和变差函数模型。为了解决这些问题，我们借用了Copula的思想，来描述没有边际分布影响的依赖结构。本文讨论了Copula函数作为地质统计学方法的方法论和基本假设，并分别采用了高斯Copula函数和非高斯Copula函数。Copula参数估计使用的多点子集和相应的似然函数的后续最大化的观测划分。插值是用两种不同的Copula进行的，其中期望值和中值是从以附近观测值为条件的Copula计算的。完整的条件Copula提供了未观测位置的估计分布，并可用于定义依赖于观测几何和值的置信区间。在巴登-符腾堡州的一个大规模的地下水水质测量网络的观测结果被用来证明的方法。研究了地下水的氯化物、硝酸盐、pH值、硫酸盐和溶解氧五个水质参数。所有五个参数均表现出非高斯依赖性。基于Copula的插值结果的五个参数进行了比较，传统的普通和指示克里金的结果。不同的统计措施，包括均方误差，相对差异和概率得分被用来比较交叉验证和分裂抽样的插值方法的结果。非高斯Copula函数比地统计插值函数的结果更好。置信区间的验证表明，它们比普通克里金法获得的估计方差更真实。
In many applications of geostatistical methods, the dependence structure of the investigated parameter is described solely with the variogram or covariance functions, which are susceptible to measurement anomalies and implies the assumption of Gaussian dependence. Moreover the kriging variance respects only observation density, data geometry and the variogram model. To address these problems, we borrow the idea from copulas, to depict the dependence structure without the influence of the marginal distribution. The methodology and basic hypotheses for application of copulas as geostatistical methods are discussed and the Gaussian copula as well as a non-Gaussian copula are used in this paper. Copula parameters are estimated using a division of the observations into multipoint subsets and a subsequent maximization of the corresponding likelihood function. The interpolation is carried out with two different copulas, where the expected and median values are calculated from the copulas conditioned with the nearby observations. The full conditional copulas provide the estimation distributions for the unobserved locations and can be used to define confidence intervals which depend on both the observation geometry and values. Observations of a large scale groundwater quality measurement network in Baden-Wurttemberg are used to demonstrate the methodology. Five groundwater quality parameters: chloride, nitrate, pH, sulfate and dissolved oxygen are investigated. All five parameters show non-Gaussian dependence. The copula-based interpolation results of the five parameters are compared to the results of conventional ordinary and indicator kriging. Different statistical measures including mean squared error, relative differences and probability scores are used to compare cross validation and split sampling results of the interpolation methods. The non-Gaussian copulas give better results than the geostatistical interpolations. Validation of the confidence intervals shows that they are more realistic than the estimation variances obtained by ordinary kriging.