Studies have shown that numerical models display the characteristics of chaotic systems, and that the solutions can be sensitive to the initial conditions, the model used, or the parameterizations used. Using the Kain-Fritsch, Grell, and modified Kuo convective parameterizations in the MASS and the WRF model, the results from a case study show that 48-h forecasts were not identical. Lyapunov exponents were calculated by plotting forecast trajectories in a phase diagram and estimating the rate of trajectory divergence for two time periods outside the study of the main cyclone. These calculations did show divergence at a rate which was consistent with differences in model height in 48-h forecasts from other studies. Additionally, the integrated enstrophy can be used to estimate the Lyapunov value. Finally, a qualitative analysis comparing various model runs (pseudo-ensemble) was performed to determine if there were regions or areas where consistent differences in the runs existed between the indexes used for forecasting convective precipitation. Results demonstrated that the region of the southeast United States associated with the developing cyclone showed the most significant differences in these indexes and for heights and temperatures. The differences in the model forecasts between convective parameterizations (intramodel forecasts) in this case were not as great as the model-to-model forecast differences (intermodel forecasts).

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