Impact of the Mesoscale Range on Error Growth and the Limits to Atmospheric Predictability

Global numerical weather prediction (NWP) models have begun to resolve the mesoscale -5/3 range of the kinetic energy (KE) spectrum, which is known to impose an inherently finite range of predictability per se as errors develop more rapidly on these scales than on the larger scales (Lorenz 1969; Rotunno and Snyder 2008). However, the dynamics of these errors under the influence of the synoptic-scale -3 range is little studied. As the error dynamics is largely constrained by the KE spectrum rather than by the model’s dynamics itself (Rotunno and Snyder 2008), idealized models with the appropriate spectra can provide a valuable insight to the error dynamics when the -5/3 range is better resolved in the future. The present work examines the error-growth behavior in a series of identical-twin perturbation experiments using an idealized two-dimensional barotropic turbulence model at a range of resolutions. The synoptic-scale -3 range of the KE spectrum gradually transitions into a -5/3 range in the mesoscale, which is increasingly resolved as the model resolution increases. The error is fitted to the scale-dependent parametric error-growth model of Žagar et al. (2017) and the relationships of the parameters across the scales are analyzed. By examining the dependence of such relationships on the model resolution and perturbation scale, the predictability limit is explored, and implications for the effectiveness of resolution-increases in NWP models are discussed.