Sensitivity of Intrinsic Error Growth to Large-Scale Uncertainty Structure in a Record-Breaking Summertime Rainfall Event

Abstract

Abstract 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 Statement This 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.