A novel analytical deep-convection updraught model and how it compares against observations

Deep moist convective updraughts are associated with various severe weather hazards, including hail formation, heavy precipitation, strong surface winds and turbulence. Yet, the actually realised hazards critically depend not only on the updraught strength, but also on the specific evolution related to the associated organised convective storm. A low-dimensional model of the governing updraught dynamics would potentially benefit parametrisations and short-term forecasting. However, despite ongoing efforts no satisfying low-dimensional model has been proposed so far. In this talk, we present a novel approach to deep-convective updraught modelling, motivated by the cauliflower-like visual appearance of cumulus clouds in the atmosphere. This appearance readily suggests that cumulus convection is the consequence of the collective dynamics of a large number of similar bubble-like elementary entities. Our model considers a central parcel that evolves according to classical parcel theory but is dynamically coupled to an ensemble of surrounding parcels. All parcels are modelled as (nonlinear, non-harmonic) oscillators. In the limit of very many interacting parcels, we adopt an approach from statistical physics to reduce the multi-body problem to a low-dimensional representation of the central-parcel evolution in terms of a generalised Langevin equation. This model essentially describes deep-convection updraughts as a Brownian motion in a potential well representing buoyancy. In particular, coupling of the central parcel to the environment causes a damping and (stochastic) forcing. We show that the model qualitatively agrees with well-reported features of atmospheric deep convection. For the quantitative assessment of our model, we compare with updraught measurements reported in the literature and those estimated from cumulus cloud-top cooling rates in geostationary satellite imagery. In particular, we give an account on the difficulties involved in directly comparing analytical models with these observations. Overall, we show that our updraught model correctly reproduces the governing features observed in atmospheric deep convection by correcting classical parcel theory. These results are encouraging and may stimulate new modelling attempts in the future.