Modelling uncertainty using stochastic transport noise in a 2-layer quasi-geostrophic model

TL;DR

This paper introduces a stochastic parameterisation method for a two-layer quasi-geostrophic model, effectively capturing unresolved scale uncertainties and improving ensemble predictions in geophysical fluid simulations.

Contribution

It presents a novel approach for estimating stochastic forcing from high-resolution data and demonstrates its effectiveness in modeling uncertainty in geophysical flows.

Findings

The stochastic parameterisation improves ensemble forecast accuracy.

It effectively captures uncertainty in both homogeneous and heterogeneous flows.

The method provides a foundation for data assimilation in geophysical models.

Abstract

The stochastic variational approach for geophysical fluid dynamics was introduced by Holm (Proc Roy Soc A, 2015) as a framework for deriving stochastic parameterisations for unresolved scales. This paper applies the variational stochastic parameterisation in a two-layer quasi-geostrophic model for a beta-plane channel flow configuration. We present a new method for estimating the stochastic forcing (used in the parameterisation) to approximate unresolved components using data from the high resolution deterministic simulation, and describe a procedure for computing physically-consistent initial conditions for the stochastic model. We also quantify uncertainty of coarse grid simulations relative to the fine grid ones in homogeneous (teamed with small-scale vortices) and heterogeneous (featuring horizontally elongated large-scale jets) flows, and analyse how the spread of stochastic solutions depends on different parameters of the model. The parameterisation is tested by comparing it with the true eddy-resolving solution that has reached some statistical equilibrium and the deterministic solution modelled on a low-resolution grid. The results show that the proposed parameterisation significantly depends on the resolution of the stochastic model and gives good ensemble performance for both homogeneous and heterogeneous flows, and the parameterisation lays solid foundations for data assimilation.