Increasing model vertical resolution may not necessarily lead to improved atmospheric predictability.

The widely accepted existence of an inherent limit of atmospheric predictability is usually attributed to weather's sensitive dependence on initial conditions. This signature feature of chaos was first discovered in the Lorenz system, initially derived as a simplified model of thermal convection. In a recent study of a high-dimensional generalization of the Lorenz system, it was reported that the predictability of its chaotic solutions exhibits a non-monotonic dimensional dependence. Since raising the dimension of the Lorenz system is analogous to refining the model vertical resolution when viewed as a thermal convection model, it is questioned whether this non-monotonicity is also found in numerical weather prediction models. Predictability in the sense of sensitive dependence on initial conditions can be measured based on deviation time, that is, the time of threshold-exceeding deviations between the solutions with minute differences in initial conditions. Through ensemble experiments involving both the high-dimensional generalizations of the Lorenz system and real-case simulations by a numerical weather prediction model, this study demonstrates that predictability can depend non-monotonically on model vertical resolution. Further analysis shows that the spatial distribution of deviation time strongly contributes to this non-monotonicity. It is suggested that chaos, or sensitive dependence on initial conditions, leads to non-monotonic dependence on model vertical resolution of deviation time and, by extension, atmospheric predictability.

Existence of multiple scales in uncertainty of numerical weather prediction.

Numerical weather prediction provides essential information of societal influence. Advances in the initial condition estimation have led to the improvement of the prediction skill. The process to produce the better initial condition (analysis) with the combination of short-range forecast and observation over the globe requires information about uncertainty of the forecast results to decide how much observation is reflected to the analysis and how far the observation information should be propagated. Forecast ensemble represents the error of the short-range forecast at the instance. The influence of observation propagating along with forecast ensemble correlation needs to be restricted by localized correlation function because of less reliability of sample correlation. So far, solitary radius of influence is usually used since there has not been an understanding about the realism of multiple scales in the forecast uncertainty. In this study, it is explicitly shown that multiple scales exist in short-range forecast error and any single-scale localization approach could not resolve this situation. A combination of Gaussian correlation functions of various scales is designed, which more weighs observation itself near the data point and makes ensemble perturbation, far from the observation position, more participate in decision of the analysis. Its outstanding performance supports the existence of multi-scale correlation in forecast uncertainty.