Transform to Entrainment Form

This post is a summary of the method I use to transform MSE spectrum mass flux histogram data to a form using a model of entrainment so that entrainment rate is on the abscissa, not MSE.

Note that the MSE spectrum mass flux histogram data represents the NET mass flux occurring at a particular MSE. If one parcel with a MSE of 340 K is moving up by 1 m/s, and another 340 K MSE parcel is moving down by 1 m/s, the net mass flux is zero. Let us consider only those MSE values with positive net mass flux, as shown in the figure below. Also plotted is a black line representing the saturation MSE which I will refer to as h*. Not it is found at each level by calculating the average temperature of all points, finding what value of water vapor mixing ratio would be saturation at that temperature, and finding the MSE based on that information. If a parcel of air has a higher MSE than this value, it will be buoyant, thus horizontal distance from the profile is a measure of buoyancy. Note the true buoyancy of a parcel would be relative to its local environment, not an average that includes even the parcel under consideration, but nevertheless the approximation is useful.

Also plotted above is a vertical line at the MSE of the maximum net mass flux, 342.7 K. This will be the "plume" considered to initiate in our entrainment model. If there were no entrainment (and no freezing, but ignore that here as an approximation) a parcel with the initial plume properties would rise with constant MSE of 342.7 K and continue to be buoyant with respect to the h* line until just below 15 km where the lines intersect. Let us consider what would happen if the parcel did mix with an average environment MSE profile, as plotted below.