The ensemble technique has been widely used in numerical weather prediction and extended-range forecasting.Current approaches to evaluate the predictability using the ensemble technique can be divided into two major g...The ensemble technique has been widely used in numerical weather prediction and extended-range forecasting.Current approaches to evaluate the predictability using the ensemble technique can be divided into two major groups.One is dynamical,including generating Lyapunov vectors,bred vectors,and singular vectors,sampling the fastest error-growing directions of the phase space,and examining the dependence of prediction efficiency on ensemble size.The other is statistical,including distributional analysis and quantifying prediction utility by the Shannon entropy and the relative entropy.Currently,with simple models,one could choose as many ensembles as possible,with each ensemble containing a large number of members.When the forecast models become increasingly complicated,however,one would only be able to afford a small number of ensembles,each with limited number of members,thus sacrificing estimation accuracy of the forecast errors.To uncover connections between different information theoretic approaches and between dynamical and statistical approaches,we propose an (∈;T)-entropy and scale-dependent Lyapunov exponent——based general theoretical framework to quantify information loss in ensemble forecasting.More importantly,to tremendously expedite computations,reduce data storage,and improve forecasting accuracy,we propose a technique for constructing a large number of "pseudo" ensembles from one single solution or scalar dataset.This pseudo-ensemble technique appears to be applicable under rather general conditions,one important situation being that observational data are available but the exact dynamical model is unknown.展开更多
为了探索交通流变化是否具有分形特性,首先利用小波分析对交通流时间序列中的分形特性进行了初步的实证和理论分析。在此基础上,对交通流时间序列进行了R/S(Re-scale Range Analysis)分析,以侦测交通流长程相关性。最后,对该交通流时间...为了探索交通流变化是否具有分形特性,首先利用小波分析对交通流时间序列中的分形特性进行了初步的实证和理论分析。在此基础上,对交通流时间序列进行了R/S(Re-scale Range Analysis)分析,以侦测交通流长程相关性。最后,对该交通流时间序列的关联维数和Kolmogorov熵进行了计算。研究结果表明,交通流变化具有分形特性。这一结论对交通流理论建模、交通流短时预测和交通管控策略的制定具有重要的意义.展开更多
We review the previous attempts of rational subgrid-scale （SGS） modelling by employing theKolmogorov equation of filtered quantities. Aiming at explaining and solving the underlyingproblems in these models, we ...We review the previous attempts of rational subgrid-scale （SGS） modelling by employing theKolmogorov equation of filtered quantities. Aiming at explaining and solving the underlyingproblems in these models, we also introduce the recent methodological investigations for therational SGS modelling technique by defining the terms of assumption and restriction. Thesemethodological works are expected to provide instructive criterions for not only the rational SGSmodelling, but also other types of SGS modelling practices.展开更多
基金Project supported by the National Science Foundation (Nos.CMMI-0825311,CMMI-0826119)
文摘The ensemble technique has been widely used in numerical weather prediction and extended-range forecasting.Current approaches to evaluate the predictability using the ensemble technique can be divided into two major groups.One is dynamical,including generating Lyapunov vectors,bred vectors,and singular vectors,sampling the fastest error-growing directions of the phase space,and examining the dependence of prediction efficiency on ensemble size.The other is statistical,including distributional analysis and quantifying prediction utility by the Shannon entropy and the relative entropy.Currently,with simple models,one could choose as many ensembles as possible,with each ensemble containing a large number of members.When the forecast models become increasingly complicated,however,one would only be able to afford a small number of ensembles,each with limited number of members,thus sacrificing estimation accuracy of the forecast errors.To uncover connections between different information theoretic approaches and between dynamical and statistical approaches,we propose an (∈;T)-entropy and scale-dependent Lyapunov exponent——based general theoretical framework to quantify information loss in ensemble forecasting.More importantly,to tremendously expedite computations,reduce data storage,and improve forecasting accuracy,we propose a technique for constructing a large number of "pseudo" ensembles from one single solution or scalar dataset.This pseudo-ensemble technique appears to be applicable under rather general conditions,one important situation being that observational data are available but the exact dynamical model is unknown.
文摘为了探索交通流变化是否具有分形特性,首先利用小波分析对交通流时间序列中的分形特性进行了初步的实证和理论分析。在此基础上,对交通流时间序列进行了R/S(Re-scale Range Analysis)分析,以侦测交通流长程相关性。最后,对该交通流时间序列的关联维数和Kolmogorov熵进行了计算。研究结果表明,交通流变化具有分形特性。这一结论对交通流理论建模、交通流短时预测和交通管控策略的制定具有重要的意义.
基金supported by the National Natural Science Foundation of China (11772032, 11572025, and 51420105008)
文摘We review the previous attempts of rational subgrid-scale （SGS） modelling by employing theKolmogorov equation of filtered quantities. Aiming at explaining and solving the underlyingproblems in these models, we also introduce the recent methodological investigations for therational SGS modelling technique by defining the terms of assumption and restriction. Thesemethodological works are expected to provide instructive criterions for not only the rational SGSmodelling, but also other types of SGS modelling practices.
