Hao Fu, Morgan O'Neill

Tropical deep convection plays a key role at the tropical depression stage of tropical cyclogenesis by aggregating vorticity, but no existing theory can depict such a stochastic vorticity aggregation process. Vorticity probability distribution function (PDF) is proposed as a tool to predict the horizontal structure and wind speed of the tropical depression, a tropical cyclone in its early stage. The reason lies in the tendency for a vortex to adjust to an axisymmetric and monotonic vorticity structure. Assuming deep convection as independent and uniformly distributed vortex tube stretching events in the lower troposphere, repetitive vortex tube stretching will make the air column area shrink many times and significantly increase vorticity. A theory of vorticity PDF is established by modelling the random stretching process as a Markov chain. The PDF turns out to be a weighted Poisson distribution, in good agreement with a randomly-forced divergent barotropic model (weak temperature gradient model), and in rough agreement with a cloud-permitting simulation. The result shows that a strong and sparse deep convective mode tends to produce more high vorticity air columns, which favors tropical cyclogenesis.