A study on multi-scale singular vector initial perturbation method for ensemble prediction

This study aims to further improve the GRAPES(Global Regional Assimilation and Prediction Enhanced System) region ensemble prediction singular vector（SV） initial perturbation method. According to the multi-scale characteristics of atmospheric initial errors, the singular vectors with different spatial resolutions and optimal time intervals are calculated from GRAPES global singular vectors. The linear combination method based on Gaussian distribution is used to construct initial perturbations based on multi-scale singular vectors to represent the fastest growing multi-scale initial errors mode in phase space. The perturbation characteristics and the ensemble prediction effects of the single-scale singular vectors initial perturbation method and multi-scale initial perturbation method are compared by conducting initial perturbation experiments for a case occurred on 19 January 2019. The main conclusions are as follows: The multi-scale singular vector initial perturbation method is able to provide reasonable initial perturbation field for regional ensemble prediction. The magnitude of the perturbation increases with time and the spatial distribution reflects the baroclinic instability of the atmosphere. In addition, multi-scale singular vector perturbations can effectively describe the error characteristics of large scale and small scale motions, and can reflect more uncertain information of initial field than single scale singular vector perturbations. The analysis of experiments results shows that GRAPES multi-scale singular vector ensemble forecast has certain advantages on consistency, CRPS （continuous ranked probability score）, outlier score, etc., and its forecasting skills are better than the single-scale singular vector method. Therefore, the multi-scale singular vector initial perturbation method based on GRAPES can improve the forecasting effect of ensemble prediction, and it can provide a scientific evidence and application basis for constructing a complete GRAPES regional singular vector ensemble forecasting system.