Study On Multi-scale Singular Vector Initial Perturbation Method For Ensemble Prediction

The initial value perturbation method of ensemble prediction is an important means to describe the uncertainty of the initial value error of numerical models.It is also the core technology in the field of ensemble prediction research.Singular Vectors(SVs)is one of the widely used initial value perturbation methods in the world.However,tangential linear and adjoint models with lower resolution are generally used to obtain singular vectors currently.This is insufficient to represent the multi-spatial-temporal scale features of the initial value error.Therefore,researching the multi-scale singular vector initial value perturbation method,which represents the multi-scale characteristics of the model initial error,has important scientific significance and application value.Based on the GRAPES-REPS(Global and Regional Assimilation and Prediction Enhanced System-Regional Ensemble Prediction System)regional ensemble prediction model,this paper designs a multiscale singular vector initial value perturbation calculation scheme for GRAPES regional ensemble prediction.Using GRAPES global singular vector calculation technology,the integration area of GRAPES regional ensemble prediction model is used as the calculation target area of singular vectors.By calculating the singular vectors of the three spatial resolutions of 2.5 ° resolution,1.5 ° resolution and 0.5 ° resolution,the initial perturbation structure with the fastest growth of the initial value error of the system at different scales in the phase space is obtained respectively.Furthermore,the linear combination method of Gaussian sampling technique was used to construct the multi-scale singular vector initial value perturbation structure of GRAPES regional ensemble prediction,and the three-dimensional structure of initial value perturbation was finally obtained through the scaled amplification factor.A multi-scale singular vector initial value perturbation ensemble prediction experiment was conducted for a total of 8 days from January 19 to January 26,2019.The perturbation characteristics and prediction result of the single-scale SVs initial value perturbation method and the multi-scale initial value perturbation method are compared and analyzed.Further,the multiscale singular vector initial value perturbation method and the Global ensemble prediction system(GEPS)down-scale initial value method are compared.The main conclusions reached are as follows:(1)Analysis of multiscale singular vector features reveals that the higher the spatial resolution,the greater the singular value,and the faster the error perturbation grows in phase space.And the optimization time interval for selecting singular vectors of different scales is different.The SVs structure calculated based on the total energy norm can well reflect the characteristics of baroclinic instability in the vertical troposphere in the mid-high latitude atmosphere in China.The large-valued regions of SVs energy norm are mainly distributed in the atmospheric troposphere.The vertical distribution of small-scale SV energy norm is concentrated,with kinetic energy as the main form,and the vertical distribution of large-scale SV energy norm is more dispersed,and the potential energy accounts for most of the total energy.(2)The structure of the initial value perturbation of GRAPES regional ensemble prediction based on multi-scale singular vectors is reasonable.The magnitude of the perturbation increases with time,which better reflects baroclinic instability characteristics of the atmosphere.In addition,the multi-scale singular vector perturbation can describe the large?medium and small scale atmospheric motion error characteristics to a certain extent,and it better represents the multi-scale uncertain information of the initial field.From the analysis of perturbation energy spectrum,the initial perturbation generated by multi-scale SVs contains the perturbation energy of multiple scales in the initial field more comprehensively.The time evolution characteristics of the perturbation energy spectrum show that with the extension of the integration time of the numerical model,small-scale perturbation energy tends to propagate to larger scales.(3)Multiple ensemble prediction test scores such as ensemble consistency,continuous grade probability score,and outlier are calculated for GRAPES-REPS regional ensemble prediction continuous experiment.The results show that the 1.5 ° SVs initial value perturbation method has better prediction effect in the single-scale SV initial value perturbation methods.The multi-scale SVs initial value perturbation method is obviously superior to the single-scale SV initial value perturbation methods.It is also superior to the GRAPES global ensemble prediction dynamic downscaling initial value perturbation method.It can not only reduce the root-mean-square error and the outlier of the ensemble prediction system,improve the spread,but also improve the probability forecasting techniques of precipitation to a certain extent.In general,the multi-scale singular vector initial value perturbation method based on GRAPES global singular vector technology can improve the prediction effect of GRAPES regional ensemble prediction.It can provide a certain scientific basis and application basis for constructing a unified GRAPES global and regional ensemble prediction singular vector perturbation method.