This paper focuses on statistical modelling using additive Gaussian process (GP) models and their efficient implementation for large-scale spatio-temporal data with a multi-dimensional grid structure. To achieve this, we exploit the Kronecker product structures of the covariance kernel. While this method has gained popularity in the GP literature, the existing approach is limited to covariance kernels with a tensor product structure and does not allow flexible modelling and selection of interaction effects. This is considered an important component in spatio-temporal analysis. We extend the method to a more general class of additive GP models that accounts for main effects and selected interaction effects. Our approach allows for easy identification and interpretation of interaction effects. The proposed model is applied to the analysis of NO$_2$ concentrations during the COVID-19 lockdown in London. Our scalable method enables analysis of large-scale, hourly-recorded data collected from 59 different stations across the city, providing additional insights to findings from previous research using daily or weekly averaged data.

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