Predictability and Error Propagation 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 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 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 demonstrate the effects of large- and small-scale perturbations in two new contexts: idealized thunderstorms under varying amounts of forcing by vertical wind shear, and real-data simulations of a deep convective event 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 case further demonstrates the relative insensitivity of storm-scale predictability thresholds to the horizontal scale of the initial errors. Hence forecasts of a wide spectrum of weather phenomena would benefit more from reducing large-scale errors in forecast initialization than from potentially expensive efforts to minimize very small-scale features in data assimilation.