  Can we improve machine-learning (ML) emulators with synthetic data? If data
are scarce or expensive to source and a physical model is available,
statistically generated data may be useful for augmenting training sets
cheaply. Here we explore the use of copula-based models for generating
synthetically augmented datasets in weather and climate by testing the method
on a toy physical model of downwelling longwave radiation and corresponding
neural network emulator. Results show that for copula-augmented datasets,
predictions are improved by up to 62 % for the mean absolute error (from 1.17
to 0.44 W m$^{-2}$).

Machine Learning;Atmospheric and Oceanic Physics