Moist convective memory in terms of thermodynamic joint probability distributions

Convective memory describes the extent to which current convective state is dependent on prior states. A linear state space model can predict the evolution of horizontal mean profiles and attempts to capture convective memory in its latent space. These state space models rely on black-box model structures to produce responses, which necessitate additional approaches to interpret causes of convective behavior.

To this end, for a more physically-interpretable approach to the latent state and its dynamics, we use probability distribution function (PDF) or histograms of idealized cloud-resolving model simulations. These PDFs, which contain joint distributions of thermodynamic variables, including temperature and moisture, provide more information than horizontal averages. This representation allows for a more physical picture of the latent state, while still avoiding the complexity of the three-dimensional spatial domain. We can further reduce the data volume by applying dimensional reduction techniques. 

By observing the PDF correspondence to temperature and moisture tendencies and other convective effects, we will attempt to use these physical insights to predict time series of horizontal mean profiles, including the nonlinear response of atmospheric perturbations.