An idealised fluid model of Numerical Weather Prediction: dynamics and data assimilation

The dynamics of the atmosphere span a tremendous range of spatial and temporal scales which presents a great challenge to those who seek to forecast the weather. To aid understanding of and facilitate research into such complex physical systems, `idealised' models can be developed that embody essential characteristics of these systems. This thesis concerns the development of an idealised fluid model of convective-scale Numerical Weather Prediction (NWP) and its use in inexpensive data assimilation (DA) experiments. The model modifies the rotating shallow water equations to include some simplified dynamics of cumulus convection and associated precipitation, extending the model of Wuersch and Craig (2014). Despite the non-trivial modifications to the parent equations, it is shown that the model remains hyperbolic in character and can be integrated accordingly using a discontinuous Galerkin finite element method for nonconservative hyperbolic systems of partial differential equations. Combined with methods to ensure well-balancedness and non-negativity, the resulting numerical solver is novel, efficient, and robust. Classical numerical experiments in shallow water theory, based on the Rossby geostrophic adjustment problem and non-rotating flow over topography, elucidate the model's distinctive dynamics, including the disruption of large-scale balanced flows and other features of convecting and precipitating weather systems. When using such intermediate-complexity models for DA research, it is important to justify their relevance in the context of NWP. A well-tuned observing system and filter configuration is achieved using the ensemble Kalman filter that adequately estimates the forecast error and has an average observational influence similar to NWP. Furthermore, the resulting error-doubling time statistics reflect those of convection-permitting models in a cycled forecast-assimilation system, further demonstrating the model's suitability for conducting DA experiments in the presence of convection and precipitation. In particular, the numerical solver arising from this research provides a useful tool to the community and facilitates other studies in the field of convective-scale DA research.