A unifying moist shallow water framework and test cases for moist shallow water models

The rotating shallow water equations are widely used in the development of weather and climate models. They are a much simpler equation set than the full 3D atmospheric equations and so are computationally cheap, but they still retain many pertinent features of atmospheric dynamics. The usual shallow water equations model a ‘dry’ atmosphere and so neglect moist processes and moisture effects. Including moisture in the shallow water system not only extends the modelling potential of the equations, but also introduces numerical complexities that are of interest in the development of time-stepping schemes. These include features such as new timescales related to moist physics processes, discontinuities introduced by the notion of boundaries between ‘precipitating’ and ‘non-precipitating’ regions, and how the addition of moisture affects the ideas of balance and conservation in the equations. In this way the moist shallow water equations provide a simplified equation set for exploring physics-dynamics coupling and how this coupling is handled by different time steppers.

This talk will discuss our implementation of a flexible, unifying moist shallow water model that encompasses three different approaches to moist shallow water modelling. Our implementation is in the dynamical core toolkit Gusto, which follows a compatible finite element approach like that of the next-generation UK Met Office model. We will demonstrate some simple moist shallow water test cases using each of the three approaches with our unifying formulation in Gusto, and describe progress towards running tests with more complex dynamics to investigate questions about time-stepping with physics.