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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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Sensitivity of Intrinsic Error Growth to Large-Scale Uncertainty Structure in a Record-Breaking Summertime Rainfall Event
It is recognized that the atmosphere’s predictability is intrinsically limited by unobservably small uncertainties that are beyond our capability to eliminate. However, there have been discussions in recent years on whether forecast error grows upscale (small-scale error grows faster and transfers to progressively larger scales) or up-amplitude (grows at all scales at the same time) when unobservably small-amplitude initial uncertainties are imposed at the large scales and limit the intrinsic predictability. This study uses large-scale small-amplitude initial uncertainties of two different structures—one idealized, univariate, and isotropic, the other realistic, multivariate, and flow dependent—to examine the error growth characteristics in the intrinsic predictability regime associated with a record-breaking rainfall event that happened on 19–20 July 2021 in China. Results indicate upscale error growth characteristics regardless of the structure of the initial uncertainties: the errors at smaller scales grow fastest first; as the forecasts continue, the wavelengths of the fastest error growth gradually shift toward larger scales with reduced error growth rates. Therefore, error growth from smaller to larger scales was more important than the growth directly at the large scales of the initial errors. These upscale error growth characteristics also depend on the perturbed and examined quantities: if the examined quantity is perturbed, then its errors grow upscale; if there is no initial uncertainty in the examined quantity, then its errors grow at all scales at the same time, although its smaller-scale errors still grow faster for the first several hours, suggesting the existence of the upscale error growth. Significance StatementThis study compared the error growth characteristics associated with the atmosphere’s intrinsic predictability under two different structures of unobservably small-amplitude, large-scale initial uncertainties: one idealized, univariate, and isotropic, the other realistic, multivariate, and flow dependent. The characteristics of the errors growing upscale rather than up-amplitude regardless of the initial uncertainties’ structure are apparent. The large-scale errors do not grow if their initial amplitudes are much bigger than the small-scale errors. This study also examined how the error growth characteristics will change when the quantity that is used to describe the error growth is inconsistent with the quantity that contains uncertainty, suggesting the importance of including multivariate, covariant uncertainties of state variables in atmospheric predictability studies.
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- Award ID(s):
- 1712290
- PAR ID:
- 10476453
- Publisher / Repository:
- JAS
- Date Published:
- Journal Name:
- Journal of the Atmospheric Sciences
- Volume:
- 80
- Issue:
- 5
- ISSN:
- 0022-4928
- Page Range / eLocation ID:
- 1415 to 1432
- 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-22-0231.1
