Using a passive tracer, entrainment is studied in cloud-resolving simulations of oceanic deep convection in radiative-convective equilibrium. It is found that the convective flux of undiluted parcels decays with height exponentially, indicating a constant probability per vertical distance of mixing with environmental air. This probability per distance is sufficiently large that undiluted updrafts are negligible above a height of 4-5 kilometers and virtually absent above 10 kilometers. These results are shown to be independent of the horizontal grid size within the range of 3.2 kilometers to 100 meters. Plumes that do reach the tropopause are found to be highly diluted.
The mass flux of undiluted cloud as observed in the large-eddy simulation (solid) decays much more rapidly than than is assumed in the Raymond-Blyth and Emanuel-Zivkovic-Rothman convective parameterizations (bounded by dashed and dotted).
An equivalent potential temperature is defined that is exactly conserved for all adiabatic transformations, including those with ice. Using this conserved variable, the density of adiabatic parcels with and without fusion can be calculated. When an adiabatic parcel is taken to sufficiently low pressures, the effect of fusion is to make the parcel more dense, not less; at the slightly higher pressures corresponding to the tropopause, the effect of fusion on buoyancy is negligible. Nevertheless, the contribution from fusion to an adiabatic parcel's kinetic energy is quite large.
Using an ensemble of tracers, it is shown how information can be encoded in parcels at the cloud base and decoded where the parcel is observed in the free troposphere. Using this technique, tropospheric clouds can be diagnosed for their cloud-base temperature, specific humidity, and vertical velocity. Using these as the initial values for a Lagrangian parcel model, it is shown that fusion provides the kinetic energy required for diluted parcels to reach the tropopause.