Three-dimensional proper orthogonal decomposition reduced-order model of the global atmospheric climate

A reduced-order model (ROM) of the global atmosphere is developed by projecting the hydrostatic equations of motion onto three-dimensional proper orthogonal decomposition (POD) modes. This approach transforms a system of partial differential equations dependent upon time and space, into a system of ordinary differential equations dependent upon only time and POD mode index. This massively reduces the dimensionality of the problem. Here we adopt the Climate Analysis Forecast Ensemble reanalysis dataset (CAFE-60), comprising of 96 realisations of the dynamically coupled atmosphere and ocean each month. Two POD bases are calculated from the atmospheric data, one for the velocity vector field, and another for the scalar temperature field. The POD ROM coefficients are calculated using a regression approach, with model errors accounted for via stochastic parameterisation. Temporal integrations of the POD ROM with dynamically coupled temperature and velocity fields are undertaken over a recent 40-year period. The statistical properties of the underlying data are broadly reproduced within the resolved modes for a range of truncation levels. Additionally, as more modes are retained in the POD ROM, the correlation of surface variance maps between the underlying data and the spatially reconstructed POD ROM output, approaches unity. The POD ROM coefficient learning and temporal integrations are completed in minutes on a laptop, as compared to the months of supercomputer time required to generate CAFE-60. • Our reduced-order model (ROM) of the global atmosphere encodes the laws of nature. • ROM coefficients are learnt from simulations corrected with real-world measurements. • The computationally cheap ROM reproduces statistics of the underlying climate data.