Stochastic parameterisation: the importance of nonlocality and memory

TL;DR

This paper examines how locality assumptions like Markovianity affect stochastic parameterisations in Earth system models, showing that nonlocality and memory improve predictions and long-term statistics, with a simple modification enhancing performance.

Contribution

It introduces a simple modification to Markovian parameterisations that improves predictive skill and reduces computational cost, highlighting the importance of nonlocality and memory.

Findings

Locality assumptions are detrimental to predictive performance.

A simple modification to Markovian models improves accuracy and efficiency.

Different configurations optimize short-term prediction versus long-term statistics.

Abstract

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.