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Technological developments and open data policies have made large, global environmental datasets accessible to everyone. For analysing 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 and precipitation data on global scale and compare models with different complexities in the covariance function.