Three different cumulus parameterization schemes, representing different philosophical approaches to the problem, are incorporated into the Madala et. al Naval Research Laboratory limited area dynamical weather prediction model and tested on the 1981 McBride et. al Colorado State composite data set for developing and nondeveloping Atlantic tropical disturbances. The parameterizations are the 1974 Kuo scheme, the 1983 Krishnamurti et al. scheme used in the FSU Global Spectral Model, and version 3.0 of the 1991 Emanuel scheme. Convection is initiated in the Kuo scheme when the environment is convectively unstable and there is net moisture convergence both in the air column and in the lowest layer of the model. The FSU scheme (a modified version of the Kuo scheme) replaces the requirement for horizontal moisture convergence by one for vertical moisture convergence between a cloud base and a cloud top and includes moisture supply by sub-grid-scale processes. The Emanuel scheme makes use of a much more detailed cloud model in which convection is determined by the bouyancy of individual air parcels and account is taken of the details of how water is condensation, precipitated and transported within the convective clouds.
With suitable choices of the parameter values that one is free to select in each scheme (determined by trial and error), each proved capable of developing a hurricane from initial conditions for developing tropical disturbances, and not developing one from initial conditions for nondeveloping disturbances, although there were significant differences in the details. Use of the Emanuel scheme resulted in the strongest tropical disturbance and exhibited a great deal of isolated convective activity outside the main disturbance. This scheme was also rather sensitive to the particular choices of parameter values, causing the model to blow up for some choices within the acceptable range and resulting in significant development of the disturbance for other choices when initial conditions for nondevelopment were used. Use of the FSU scheme resulted in the weakest development. All three parameterizations were sensitive to the mean vertical temperature profile used to initialize the model. Two such profiles, based on observations published by Sheets in 1969 and Jordan in 1958, failed to produce a tropical disturbance because they lacked an adequate amount of CAPE, while the sounding used by Madala et. al in 1987 resulted in development with initial conditions for developing disturbances and nondevelopment with initial conditions for the nondeveloping disturbance.
Reasons for the differences produced by the three parameterizations are discussed and suggestions are made for pursuing this work further using optimal parameter estimation.