A Lagrangian View to the Evolution of Convective Updrafts

The representation of cumulus convection is a known source of uncertainty within current weather and climate models. Where model resolution is too coarse to accurately resolve convection, parameterisations are required to estimate the impact of small-scale convective processes. High resolution large eddy simulations (LES) can be used to diagnose many aspects of convective processes, such as heat and momentum budgets and rates of entrainment. However, LES is computationally expensive, making it impossible to use within operational models. This study aims to bridge the gap between current coarser models and LES by developing a stochastic Lagrangian model to represent an ensemble of air parcels. Vertical velocity, liquid water potential temperature, and total specific humidity are predicted following the ensemble of parcels. The random motions associated with turbulence are represented by a stochastic term within the w-tendency equation. The mean fields which the parcels interact with are defined by an ensemble average of nearby parcels. Several fixers have been developed to ensure that conservation properties are respected. At the current stage of development, the model can represent dry convective boundary layer and shallow convection cases. A theoretical study of the stochastic differential equations is useful to verify the self-consistency of the model and also as a tool for calibrating various parameters within the model. A key question for this project is how well the stochastic parcel model can replicate the statistics of LES results. This will act as a measure of the model’s success, allowing for a deeper understanding on accurately modelling convective processes. Due to the Lagrangian nature of the model, analysis can be conducted upon how the parcels’ characteristics change over time as the parcels experience smaller-scale convective processes such as entrainment. Ultimately, results from this model may yield better understandings of small-scale convective processes. This can create potential for improvements to parameterisations in operational models, reducing model uncertainty generated by convective processes.