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.
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