Abstract We investigate the sensitivity of mesoscale atmospheric predictability to the slope of the background kinetic energy spectrum E by adding initial errors to simulations of idealized moist midlatitude cyclones at several wavenumbers k for which the slope of E (k) is significantly different. These different slopes arise from 1) differences in the E (k) generated by cyclones growing in two different moist baroclinically unstable environments, and 2) differences in the horizontal scale at which initial perturbations are added, with E (k) having steeper slopes at larger scales. When small-amplitude potential temperature perturbations are added, the error growth through the subsequent 36-h simulation is not sensitive to the slope of E (k) nor to the horizontal scale of the initial error. In all cases with small-amplitude perturbations, the error growth in physical space is dominated by moist convection along frontal boundaries. As such, the error field is localized in physical space and broad in wavenumber (spectral) space. In moist midlatitude cyclones, these broadly distributed errors in wavenumber space limit mesoscale predictability by growing up-amplitude rather than by cascading upscale to progressively longer wavelengths. In contrast, the error distribution in homogeneous turbulence is broad in physical space and localized in wavenumber space, and dimensional analysis can be used to estimate the error growth rate at a specific wavenumber k from E (k). Predictability estimates derived in this manner, and from the numerical solutions of idealized models of homogeneous turbulence, depend on whether the slope of E (k) is shallower or steeper than k^ −3 , which differs from the slope-insensitive behavior exhibited by moist midlatitude cyclones.
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A New Theoretical Framework for Understanding Multiscale Atmospheric Predictability
Here we present a new theoretical framework that connects the error growth behavior in numerical weather prediction (NWP) with the atmospheric kinetic energy spectrum. Building on previous studies, our newly proposed framework applies to the canonical observed atmospheric spectrum that has a -3 slope at synoptic scales and a -5/3 slope at smaller scales. Based on this realistic hybrid energy spectrum, our new experiment using hybrid numerical models provides reasonable estimations for the finite predictable ranges at different scales. We further derive an analytical equation that helps understand the error growth behavior. Despite its simplicity, this new analytical error growth equation is capable of capturing the results of previous comprehensive theoretical and observational studies of atmospheric predictability. The success of this new theoretical framework highlights the combined effects of quasi-two-dimensional dynamics at synoptic-scales (-3 slope) and three-dimensional turbulence-like small-scale chaotic flows (-5/3 slope) in dictating the error growth. It is proposed that this new framework could serve as a guide for understanding and estimating the predictability limit in the real world.
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- Award ID(s):
- 1712290
- NSF-PAR ID:
- 10158496
- Date Published:
- Journal Name:
- Journal of the Atmospheric Sciences
- ISSN:
- 0022-4928
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1175/jas-d-19-0271.1
