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About regression-kriging: From equations to case studies

机译：关于回归克里金法：从方程式到案例研究

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This paper discusses the characteristics of regression-kriging (RK), its strengths and limitations, and illustrates these with a simple example and three case studies. RK is a spatial interpolation technique that combines a regression of the dependent variable on auxiliary variables (such as land surface parameters, remote sensing imagery and thematic maps) with simple kriging of the regression residuals. It is mathematically equivalent to the interpolation method variously called "Universal Kriging" (UK) and "Kriging with External Drift" (KED), where auxiliary predictors are used directly to solve the kriging weights. The advantage of RK is the ability to extend the method to a broader range of regression techniques and to allow separate interpretation of the two interpolated components. Data processing and interpretation of results are illustrated with three case studies covering the national territory of Croatia. The case studies use land surface parameters derived from combined Shuttle Radar Topography Mission and contour-based digital elevation models and multitemporal-enhanced vegetation indices derived from the MODIS imagery as auxiliary predictors. These are used to improve mapping of two continuous variables (soil organic matter content and mean annual land surface temperature) and one binary variable (presence of yew). In the case of mapping temperature, a physical model is used to estimate values of temperature at unvisited locations and RK is then used to calibrate the model with ground observations. The discussion addresses pragmatic issues: implementation of RK in existing software packages, comparison of RK with alternative interpolation techniques, and practical limitations to using RK. The most serious constraint to wider use of RK is that the analyst must carry out various steps in different software environments, both statistical and GIS.
机译：本文讨论了回归克里金法（RK）的特点，优势和局限性，并通过一个简单的示例和三个案例研究对其进行了说明。 RK是一种空间插值技术，将因变量对辅助变量（如地表参数，遥感影像和专题图）的回归与回归残差的简单克里金法相结合。它在数学上等同于插值方法，分别称为“通用克里格法”（UK）和“外部漂移克里格法”（KED），其中辅助预测变量直接用于求解克里金法权重。 RK的优点是能够将方法扩展到更广泛的回归技术，并能够分别解释两个内插分量。涉及克罗地亚国家领土的三个案例研究说明了数据处理和结果解释。案例研究使用从航天飞机雷达地形任务和基于轮廓的数字高程模型相结合得出的地表参数以及从MODIS影像得到的多时相增强植被指数作为辅助预测因子。这些用于改进两个连续变量（土壤有机物含量和平均年地表温度）和一个二元变量（存在紫杉）的映射。在绘制温度图的情况下，将使用物理模型来估计未访问位置的温度值，然后使用RK通过地面观察来校准模型。讨论解决了一些务实的问题：在现有软件包中实现RK，将RK与替代插值技术进行比较以及使用RK的实际限制。广泛使用RK的最严重限制是分析人员必须在不同的软件环境（统计和GIS）中执行各种步骤。

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