Stochastic parameterisation: the importance of nonlocality and memory

Stochastic parameterisations deployed in models of the Earth system frequently invoke locality assumptions such as Markovianity or spatial locality. This work highlights the impact of such assumptions on predictive performance. Both in terms of short-term forecasting and the representation of long-term statistics, we find locality assumptions to be detrimental in idealised experiments. We show, however, that judicious choice of Markovian parameterisation can mitigate errors due to assuming Markovianity. We propose a simple modification to standard Markovian parameterisations, which yields significant improvements in predictive skill while reducing computational cost. We further note a divergence between configurations of a parameterisation which perform best in short-term prediction and those which best represent time-invariant statistics.