Quantitative View on the Processes Governing the Upscale Error Growth up to the Planetary Scale Using a Stochastic Convection Scheme

Two diagnostics based on potential vorticity and the envelope of Rossby waves are used to investigate upscale error growth from a dynamical perspective. The diagnostics are applied to several cases of global, real-case ensemble simulations, in which the only difference between the ensemble members lies in the random seed of the stochastic convection scheme. Based on a tendency equation for the enstrophy error, the relative importance of individual processes to enstrophy-error growth near the tropopause is quantified. After the enstrophy error is saturated on the synoptic scale, the envelope diagnostic is used to investigate error growth up to the planetary scale. The diagnostics reveal distinct stages of the error growth: in the first 12 h, error growth is dominated by differences in the convection scheme. Differences in the upper-tropospheric divergent wind then project these diabatic errors into the tropopause region (day 0.5-2). The subsequent error growth (day 2-14.5) is governed by differences in the nonlinear near-tropopause dynamics. A fourth stage of the error growth is found up to 18 days when the envelope diagnostic indicates error growth from the synoptic up to the planetary scale. Previous ideas of the multiscale nature of upscale error growth are confirmed in general. However, a novel interpretation of the governing processes is provided. The insight obtained into the dynamics of upscale error growth may help to design representations of uncertainty in operational forecast models and to identify atmospheric conditions that are intrinsically prone to large error amplification.