Modelling non-stationary variance of soil properties by tempering an empirical spectrum
Modelling non-stationary variance of soil properties by tempering an empirical spectrum
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DOI：
10.1016/j.geoderma.2009.07.006
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发表时间：
2009-10
期刊：
影响因子：
6.1
通讯作者：
K. Haskard;R. Lark
中科院分区：
文献类型：
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作者：
K. Haskard;R. Lark
土壤性质的地质统计预测依赖于协方差的平稳性假设，但这通常是不可信的，这意味着预测可能是次优的，其计算的方差将是不可靠的。在统计文献中已经有过解决这个问题的尝试，在本文中，我们讨论、开发和评估一种方法。这是频谱调和，我们通过在空间上调整基础平稳过程的频谱来对非平稳方差进行建模。本文描述了由初始协方差矩阵的特征向量和特征值组成的经验基础上的光谱调和，以及允许我们在空间上适应相关属性、空间相关分量的方差和块金方差的修改；以及独立地适应这些。只要可以估计一些初始协方差矩阵(通常是平稳的)，该方法可以应用于来自任何维度、来自一个或多个实现、以及具有任何排列的位置的空间数据。光谱回火被应用于一氧化二氮排放和重力水分含量的案例研究，保留了一半的数据用于验证。与最优平稳模型的比较表明，克立格预测受影响较小，但非平稳模型下的预测误差方差(克立格方差)更可靠。
Geostatistical prediction of soil properties depends on the assumption of stationarity in the covariance, but this is often implausible, which implies that predictions may be suboptimal, and their computed variances will be unreliable. There have been attempts in the statistical literature to tackle this problem, and in this paper we discuss, develop and evaluate one approach. This is spectral tempering, in which we model non-stationary variances by spatially adapting the spectrum of an underlying stationary process. This paper describes spectral tempering from an empirical basis consisting of eigenvectors and eigenvalues of an initial covariance matrix, with modifications that allow us to adapt spatially the correlation properties, variance of the spatially-correlated component, and nugget variance; and to adapt these independently. The method can be applied to spatial data from any number of dimensions, from one or more realizations, and with locations in any arrangement, provided some initial covariance matrix (typically stationary) can be estimated. Spectral tempering is applied to a case study on nitrous oxide emissions and gravimetric water content, reserving half of the data for validation. Comparison with the optimal stationary model shows that kriged predictions are little affected, but prediction error variances (kriging variances) are more reliable under the non-stationary model.