空间克里金插值的时空扩展与实现

Extension and implementation from spatial-only to spatiotemporal Kriging interpolation

空间克里金插值常用来补充采样点不足的问题,当数据分布与时间和空间都有关系时,面向空间的方法直接应用到时空过程可能导致有价值信息在时间维的丢失,由此导致了时空克里金插值的研究。研究的目标是将空间插值模型扩展到时空领域并实现时空变异函数、时空插值和时空交叉验证。其方法是首先获得最佳变异函数模型和时空下的有效基台值、块金值与变程,然后实现时空克里金插值的扩展,最后通过时空交叉验证去验证扩展的时空克里金插值方法的有效性。验证结果表明,扩展的时空方法能为随机领域以一定的精度提供较多的信息,为不同时空环境下的预测或插值提供了一个有效的途径。

The spatial-only Kriging interpolation is usually used to solve the problem of shortage of sampled data. When sampled and unsampled locations are relative with time and space, it will bring about the loss of worthy data in time dimension if applying directly the spatial-only Kriging interpolation to spatiotemporal domain, which has led to the study on spatiotemporal Kriging interpolation. The goal of this paper is to extend spatial-only Kriging interpolation to spatiotemporal domain and implement the spatiotemporal variograms, spatiotemporal interpolations and spatiotemporal cross validation. Firstly the maximum likely variograms model and effective spatiotemporal sill, nugget, range were derived, secondly the spatiotemporal Kriging interpolation was implemented. Lastly cross validation was clone to test the validity of spatiotemporal interpolation. The experimental results show that the extension from spatial-only to spatiotemporal Kriging interpolation can provide enough information on random domains at certain accuracy. It provides an effective approach to spatiotemporal estimation or interpolation of various spatiotemporal phenomenon.