Parametrizing the evolution of convective updraft vertical velocities

Moisture convergence, latent heat, upper-level divergence all contribute to the genesis and growth of convective updrafts. In order to characterize the morphology of this evolution, and identify its constituent modes, we analyzed a large data set of synthetic updrafts simulated using a convection-resolving differential-equation solver run at high spatial and temporal resolutions (respectively 100 meters and 10 seconds). The analysis started by fitting each simulated updraft with a 6-parameter analytic representation, so that the joint statistics of the 6 parameters and of their evolution in time can be quantified. The first result is that an effective 6-parameter representation does exist and approximates the vertical profiles with a residual relative error whose r.m.s. value is smaller than 10% for 59% of all cases, and smaller than 20% for 89% of all cases. The r.m.s value of the absolute error is smaller than 0.4 m/s for 97% of all cases. Having established the suitability of this approximation, the variability of the 6 parameters for the 2-minute average Wa of a profile W was quantified, as was the variability of the evolution of W – Wa over a two-minute interval. The analysis reveals that 4 scalars suffice to capture the bulk of the variability of the evolution of convective updrafts. The modes (spanning the range of values of these 4 scalars) turn out to be related to the maximum amplitudes of w and to the heights at which they are achieved. This description paves the way toward the characterization of the environmental determinants of updraft evolution and, in turn, the determination of the effects of updraft characteristics on upper-level air density, divergence and the resulting anvil clouds.