Thomas Kent, Luca Cantarello , Gordon Inverarity, Steven Tobias, Onno Bokhove

To aid understanding of and facilitate research into forecast-assimilation systems of Numerical Weather Prediction (NWP), idealized models that embody essential characteristics of these systems can be used. This article concerns the use of such an idealized fluid model of convective-scale NWP in inexpensive data assimilation (DA) experiments. The forecast model, introduced in Kent et al (2017), is a modification of the rotating shallow water equations that includes some simplified dynamics of cumulus convection and associated precipitation. It is of interest owing to (i) its distinctive dynamics, including the disruption of large-scale balanced flows, highly nonlinear behaviour associated with convection and moisture, and other features of convecting and precipitating weather systems, and (ii) its computational efficiency, a crucial factor for an idealized model.
When using such intermediate-complexity models for DA research, it is important to justify their relevance in the context of NWP.
The process of achieving a well-tuned observing system and filter configuration is described here using a deterministic ensemble Kalman filter. The tuning process involves systematically permuting through parameters of the combined forecast-assimilation system, combinations of which define a single experiment. We conduct numerous experiments, each characterized by a specific combination of parameters pertaining to the filter configuration and observing system, and assess their performance and relevance objectively in a concise graphical manner. We show how to construct well-tuned experiments in which the ensemble provides a good estimate of the forecast error, assessed via a spread-error diagnostic and the Continuous Ranked Probability Score. The forecast-assimilation system has an average observational influence similar to operational NWP (about 30%) and the resulting error-doubling time statistics reflect those of operational convection-permitting models (about 6-9 hours). We supplement the objective assessment of performance and relevance with a subjective examination of model fields at different forecast lead times, illustrating the impact of data assimilation on the model dynamics and highlighting where improvements are both achieved and lacking. Our approach and results not only demonstrate the model's suitability for conducting DA experiments in the presence of convection and precipitation, but also offer a formative protocol for conducting data assimilation research in an idealized yet relevant framework.