Nell Hartney | Searcharxiv

arXiv2026

Exploring physics-dynamics coupling using moist shallow water equations

One of the key choices for numerical models of geophysical fluids is how parametrisations of physical processes interact with the numerical methods that handle the resolved flow, known in the atmospheric community as the dynamical core. As both the dynamical core and parametrisations of physics processes continue to evolve and improve, the issue of physics-dynamics coupling - how these two different parts of the model interact - becomes ever more important. In this paper we use two variations of the moist shallow water equations to develop a simplified framework that can be used to investigate some of the questions associated with physics-dynamics coupling. The shallow water equations act as a simplified dynamical core that is computationally cheap but still retains pertinent features of the atmosphere, and the introduction of moisture means the addition to the model of a physical parametrisation. This study uses 'split-physics' moist thermal shallow water equations which couple moisture to the shallow water equations via a parametrisation, and also develops a new 'integrated-physics' formulation of the moist thermal shallow water equations which re-formulates the model so that all the moist processes are captured in the dynamics. This integrated-physics model thus requires no physics-dynamics coupling and acts as a ground-truth to compare coupling strategies in the split-physics formulation against. We use both models to examine the effect of varying the approach to how physics is coupled to the dynamics in the semi-implicit quasi-Newton timestepping scheme. The results demonstrate the usefulness of the integrated-physics moist shallow water equations and provide insights into how best to deal with physics in a model's timestep.

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arXiv2024

Exploring forms of the moist shallow water equations using a new compatible finite element discretisation

The moist shallow water equations offer a promising route for advancing understanding of the coupling of physical parametrisations and dynamics in numerical atmospheric models, an issue known as 'physics-dynamics coupling'. Without moist physics, the traditional shallow water equations are a simplified form of the atmospheric equations of motion and so are computationally cheap, but retain many relevant dynamical features of the atmosphere. Introducing physics into the shallow water model in the form of moisture provides a tool to experiment with numerical techniques for physics-dynamics coupling in a simple dynamical model. In this paper, we compare some of the different moist shallow water models by writing them in a general formulation. The general formulation encompasses three existing forms of the moist shallow water equations and also a fourth, previously unexplored formulation. The equations are coupled to a three-state moist physics scheme that interacts with the resolved flow through source terms and produces two-way physics-dynamics feedback. We present a new compatible finite element discretisation of the equations and apply it to the different formulations of the moist shallow water equations in three test cases. The results show that the models capture generation of cloud and rain and physics-dynamics interactions, and demonstrate some differences between moist shallow water formulations and the implications of these different modelling choices.

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