The non-linear relationship between buoyancy and dilution that is key to criticality can be understood by considering two parcels with identical initial conditions ascending through a depth Δz. Assuming that the environmental lapse rate that each parcel encounters through this layer is different we would expect that the vertical velocity would increase more rapidly for the parcel in the large lapse rate environment. As a result, this parcel would spend less time entraining environmental air within the layer. In contrast, the second parcel would ascend more slowly through the layer and the amount of entrainment would be larger. Entrainment will reduce parcel buoyancy below the adiabatic maximum for both parcels. However, because the amount of entrainment is larger for the second parcel, the reduction in buoyancy would be larger. The parcel would ascend more slowly further increasing the amount of entrainment. Thus a feedback exists between buoyancy and dilution. In the supercritical regime, the rate of increase in the buoyancy of a parcel as it ascends exceeds the reduction in buoyancy due to dilution and thus DCI is likely. In the subcritical regime the rate of increase in the buoyancy of a parcel as it ascends is outpaced by the rate of reduction in buoyancy from dilution and thus DCI is unlikely. Therefore, ultimately, the probability of DCI is seen to depend not on the likelihood that parcels will become unstable but on the likelihood that parcels will become supercritical.
Criticality has been tested with a small set of cloud-scale simulations, conceptualized with a heuristic Lagrangian column model, and preliminarily quantified using a laterally entraining plume (LEP) model. The goal in quantifying criticality with the LEP model is to define metrics that can be used to both solidify the concept of criticality and (more importantly) to further test the viability of using criticality for forecasting DCI. In this presentation, the concept of criticality will be introduced, preliminary results will be presented, and future work will be discussed.