Variational Stochastic Parameterisations and their Applications to Primitive Equation Models

TL;DR

This paper investigates stochastic parameterisations of the Primitive Equations using SALT and SFLT frameworks, demonstrating their effects on eddy kinetic energy and spatial spectrum, with a new calibration method and numerical implementation.

Contribution

It introduces a new calibration methodology for SFLT and compares it with SALT, enhancing stochastic parameterisation techniques for Primitive Equations.

Findings

SALT increases eddy kinetic energy and improves spatial spectrum.

SALT causes excessive downward diffusion of temperature.

SFLT shows similar but less pronounced improvements.

Abstract

We present a numerical investigation into the stochastic parameterisations of the Primitive Equations (PE) using the Stochastic Advection by Lie Transport (SALT) and Stochastic Forcing by Lie Transport (SFLT) frameworks. These frameworks were chosen due to their structure-preserving introduction of stochasticity, which decomposes the transport velocity and fluid momentum into their drift and stochastic parts, respectively. In this paper, we develop a new calibration methodology to implement the momentum decomposition of SFLT and compare with the Lagrangian path methodology implemented for SALT. The resulting stochastic Primitive Equations are then integrated numerically using a modification of the FESOM2 code. For certain choices of the stochastic parameters, we show that SALT causes an increase in the eddy kinetic energy field and an improvement in the spatial spectrum. SFLT also shows improvements in these areas, though to a lesser extent. SALT does, however, have the drawback of an excessive downwards diffusion of temperature.