Technological developments and open data policies have made large, global environmental datasets accessible to everyone. For analyzing such datasets, including spatiotemporal correlations using traditional models based on Gaussian processes does not scale with data volume and requires strong assumptions about stationarity, separability, and distance measures of covariance functions that are often unrealistic for global data. Only very few modeling approaches suitably model spatiotemporal correlations while addressing both computational scalability as well as flexible covariance models. In this paper, we provide an extension to the multi-resolution approximation (MRA) approach for spatiotemporal modeling of global datasets. MRA has been shown to be computationally scalable in distributed computing environments and allows for integrating arbitrary user-defined covariance functions. Our extension adds a spatiotemporal partitioning, and fitting of complex covariance models including nonstationarity with kernel convolutions and spherical distances. We evaluate the effect of the MRA parameters on estimation and spatiotemporal prediction using simulated data, where computation times reduced around two orders of magnitude with an increase of the root-mean-square prediction error of around five percent. This allows for trading off computation times against prediction errors, and we derive a practical strategy for selecting the MRA parameters. We demonstrate how the approach can be practically used for analyzing daily sea surface temperature data on global scale and compare models with different complexities in the covariance function.

技术的发展和开放数据政策使每个人都可以访问大型的全球环境数据集。为了分析此类数据集，包括使用基于高斯过程的传统模型进行时空相关性，并不随数据量成比例，并且需要对协方差函数的平稳性，可分离性和距离度量进行强有力的假设，而这些假设对于全局数据而言通常是不现实的。只有极少数的建模方法可以在解决计算可伸缩性以及灵活的协方差模型的同时对时空相关性进行适当的建模。在本文中，我们为全局数据集的时空建模提供了多分辨率近似（MRA）方法的扩展。MRA已显示在分布式计算环境中具有计算可伸缩性，并且允许集成任意用户定义的协方差函数。我们的扩展增加了时空划分，并拟合了复杂的协方差模型，包括带有核卷积和球面距离的非平稳性。我们使用模拟数据评估了MRA参数对估计和时空预测的影响，其中计算时间减少了大约两个数量级，均方根预测误差增加了约5％。这样可以权衡计算时间和预测误差，我们得出了选择MRA参数的实用策略。