An evolutionary spectrum approach to incorporate large‐scale geographical descriptors on global processes

Summary We introduce a non‐stationary spatiotemporal model for gridded data on the sphere. The model specifies a computationally convenient covariance structure that depends on heterogeneous geography. Widely used statistical models on a spherical domain are non‐stationary for different latitudes, but stationary at the same latitude ( axial symmetry ). This assumption has been acknowledged to be too restrictive for quantities such as surface temperature, whose statistical behaviour is influenced by large‐scale geographical descriptors such as land and ocean. We propose an evolutionary spectrum approach that can account for different regimes across the Earth's geography and results in a more general and flexible class of models that vastly outperforms axially symmetric models and captures longitudinal patterns that would otherwise be assumed constant. The model can be estimated with a multistep conditional likelihood approximation that preserves the non‐stationary features while allowing for easily distributed computations: we show how the model can be fitted to more than 20 million data points in less than 1 day on a state of the art workstation. The resulting estimates from the statistical model can be regarded as a synthetic description (i.e. a compression) of the space–time characteristics of an entire initial condition ensemble.