Predictability in Idealized and Real-Data Simulations of Deep Convection

Observations show that the kinetic energy spectrum in the atmosphere varies approximately as the wavenumber k to the -5/3 power for the mesoscale with wavelengths shorter than about 400 km. Lorenz (1969) demonstrated that rapid upscale growth of errors occurs in a system where the background kinetic energy spectrum follows this k^-5/3 power. Recent studies of idealized thunderstorms have demonstrated that a k^-5/3 kinetic energy spectrum can be produced solely by thermodynamically-driven deep convection. In this idealized setting, Durran and Weyn (2016) showed that large-scale initial errors of small amplitude and small-scale initial errors of modestly larger amplitude equally degrade the predictability of storm-scale structures beyond 3–4 hour lead times. Here we further explore the effects of large- and small-scale perturbations in two contexts: idealized thunderstorms under varying amounts of forcing by vertical wind shear, and real-data simulations of deep convective events over the southeastern United States. Idealized simulations with 10, 20, and 30 m/s of vertical wind shear in the lower 5 km all show nearly identical loss of predictability within 4–6 hours, for both small- and large-scale initial errors, despite large differences in the structure of the mesoscale convective systems produced by different shear. The real-data cases further illustrate the relative insensitivity of storm-scale predictability thresholds to the horizontal scale of the initial errors. The intrinsic limit to predictability, which is about several hours for convective scales, is estimated in these systems by examining the effect of the amplitude of initial errors on error growth. The sensitivity of error growth to model horizontal resolution and explicit diffusion are discussed, along with different metrics for evaluating the practical predictability of real-world numerical weather forecasts.