Thunderstorms and the Cascade of Energy and Error through the Mesoscale

Kolmogorov showed that the energy cascade proposed by Richardson will distribute kinetic energy (KE) among spatial scales in proportion to the wavelength to the 5/3 power. Lorenz showed that forecast errors can propagate rapidly upscale in fluid systems with background KE spectra varying like the wavelength to the 5/3 power. Observations show that the kinetic energy spectrum of the atmosphere varies in approximate proportion to the wavelength to the 5/3 power at horizontal wavelengths shorter than about 400 km. Nevertheless, the mesoscale atmospheric circulations that occur at wavelengths between 10 and 400 km are not homogeneous, isotropic and stationary as necessary for the strict application of Kolmogorov's theory, and the processes that create the observed atmospheric KE spectrum are not well understood.

Here we examine ensembles of idealized and real-world squall-line simulations. These simulations show that initial errors on scales around 100 km are more likely to extend the accuracy of forecasts at lead times longer than 3-4 hours than potentially expensive efforts to minimize initial errors on much smaller scales. These simulations also demonstrate that squall lines, triggered in a horizontally homogeneous environment with no initial background circulations, can generate a background mesoscale KE spectrum with a slope proportional the the 5/3 power of the wavelength in a manner qualitatively consistent with a 30-year-old hypothesis of Lilly that had been dismissed many recent researchers.