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An Initial Perturbation Method for the Multiscale singular vector in Global Ensemble Prediction

Advances in Atmospheric Sciences 2024年第3期41卷 545-563页

作者： Xin LIU Jing CHEN Yongzhu LIU Zhenhua HUO Zhizhen XU Fajing CHEN Jing WANG Yanan MA Yumeng HAN School of Atmospheric Sciences Nanjing University of Information Science&TechnologyNanjing 210044China Chinese Academy of Meteorological Sciences Beijing 100081China CMA Earth System Modeling and Prediction Centre(CEMC) Beijing 100081China Key Laboratory of Earth System Modeling and Prediction of China Meteorological Administration Beijing 100081China Tianjin Meteorological Observatory Tianjin 300074China China Meteorological Administration Xiong’an Atmospheric Boundary Layer Key Laboratory Hebei 071799China

Ensemble prediction is widely used to represent the uncertainty of single deterministic Numerical Weather Prediction(NWP) caused by errors in initial conditions(ICs). The traditional singular vector(SV) initial perturbation method tends only to capture synoptic scale initial uncertainty rather than mesoscale uncertainty in global ensemble prediction. To address this issue, a multiscale SV initial perturbation method based on the China Meteorological Administration Global Ensemble Prediction System(CMA-GEPS) is proposed to quantify multiscale initial uncertainty. The multiscale SV initial perturbation approach entails calculating multiscale SVs at different resolutions with multiple linearized physical processes to capture fast-growing perturbations from mesoscale to synoptic scale in target areas and combining these SVs by using a Gaussian sampling method with amplitude coefficients to generate initial perturbations. Following that, the energy norm,energy spectrum, and structure of multiscale SVs and their impact on GEPS are analyzed based on a batch experiment in different seasons. The results show that the multiscale SV initial perturbations can possess more energy and capture more mesoscale uncertainties than the traditional single-SV method. Meanwhile, multiscale SV initial perturbations can reflect the strongest dynamical instability in target areas. Their performances in global ensemble prediction when compared to single-scale SVs are shown to(i) improve the relationship between the ensemble spread and the root-mean-square error and(ii) provide a better probability forecast skill for atmospheric circulation during the late forecast period and for short-to medium-range precipitation. This study provides scientific evidence and application foundations for the design and development of a multiscale SV initial perturbation method for the GEPS.

关键词： multiscale uncertainty singular vector initial perturbation global ensemble prediction system

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Characteristics and Nonlinear Growth of the singular vector Related to a Heavy Rainfall Case over the Korean Peninsula

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Advances in Atmospheric Sciences 2012年第1期29卷 10-28页

作者： Yonghan CHOI Joowan KIM Dong-Kyou LEE School of Earth and Environmental Sciences Seoul National University

In this study, singular vectors related to a heavy rainfall case over the Korean Peninsula were calculated using the fifth-generation Pennsylvania State University-National Center for Atmospheric Research Mesoscale Model （MM5） adjoint modeling system. Tangent linear and adjoint models include moist physical processes, and a moist basic state and a moist total energy norm were used for the singular-vector calculations. The characteristics and nonlinear growth of the first singular vector were analyzed, focusing on the relationship between the basic state and the singular vector. The horizontal distribution of the initial singular vector was closely related to the baroclinicity index and the moisture availability of the basic state. The temperature-component energy at a lower level was dominant at the initial time, and the kinetic energy at upper levels became dominant at the final time in the energy profile of the singular vector. The nonlinear growth of the singular vector appropriately reflects the temporal variations in the basic state. The moisture-component energy at lower levels was dominant at earlier times, indicating continuous moisture transport in the basic state. There were a large amount of precipitation and corresponding latent heat release after that period because the continuous moisture transport created favorable conditions for both convective and nonconvective precipitation. The vertical propagation of the singular-vector energy was caused by precipitation and the corresponding latent heating in the basic state.

关键词： singular vector nonlinear growth heavy rainfall MM5 adjoint modeling system

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Differential Equations and singular vectors in Verma Modules over sl(n,C)

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Acta Mathematica Sinica,English Series 2015年第7期31卷 1057-1066页

作者： Wei XIAO College of Mathematics and Computational Science Shenzhen University

Xu introduced a system of partial differential equations to investigate singular vectors in the Verma module of highest weight λ, over sl（n,C）. He gave a differential-operator representation of the symmetric group Sn on the corresponding space of truncated power series and proved that the solution space of the system is spanned by {σ（1）｜ σ ∈ Sn}. It is known that Sn is also the Weyl group of sl（n, C） and generated by all reflections sα with positive roots α. We present an explicit formula of the solution sα（1） for every positive root α and show directly that sα（1） is a polynomial if and only if （λ＋p, α） is a nonnegative integer. From this, we can recover a formula of singular vectors given by Malikov et al..

关键词： Verma modules singular vector differential equation truncated power series

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Verma Modules over Some Lie Algebras of W-Type

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Journal of Mathematical Research with Applications 2023年第4期43卷 447-456页

作者： Congcong CHEN Yongsheng CHENG School of Mathematics and Statistics Henan University

In this paper, we describe the structure of Verma modules over the two kinds of Lie algebras g(λ) of W-type. We determine the reducibility and the singular vectors of their Verma modules under some conditions.

关键词： W-algebra Verma module singular vector

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Adjoint-based Sensitivity Analysis of a Mesoscale Low on the Mei-yu Front and Its Implications for Adaptive Observation

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Advances in Atmospheric Sciences 2007年第3期24卷 435-448页

作者：钟科董佩明赵思雄蔡其发兰伟仁 State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG) Institute of Atmospheric Physics Chinese Academy of Sciences Institute of Atmospheric Physics Chinese Academy of Sciences Institute of Meteorology PLA University of Science and Technology P.O. Box 2433

An adjoint sensitivity analysis of one mesoscale low on the mei-yu Front is presented in this paper. The sensitivity gradient of simulation error dry energy with respect to initial analysis is calculated. And after verifying the ability of a tangent linear and adjoint model to describe small perturbations in the nonlinear model, the sensitivity gradient analysis is implemented in detail. The sensitivity gradient with respect to different physical fields are not uniform in intensity, simulation error is most sensitive to the vapor mixed ratio. The localization and consistency are obvious characters of horizontal distribution of the sensitivity gradient, which is useful for the practical implementation of adaptive observation. The sensitivity region tilts to the northwest with height increasing; the singular vector calculation proves that this tilting characterizes a quick-growing structure, which denotes that using the leading singular vectors to decide the adaptive observation region is proper. When connected with simulation of a mesoscale low on the mei-yu Front, the sensitivity gradient has the following physical characters： the obvious sensitive region is mesoscale, concentrated in the middle-upper troposphere, and locates around the key system; and the sensitivity gradient of different physical fields correlates dynamically.

关键词： adjoint sensitivity analysis singular vector adaptive observation mei-yu front mesoscale low

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Applications of Conditional Nonlinear Optimal Perturbation to the Study of the Stability and Sensitivity of the Jovian Atmosphere

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Advances in Atmospheric Sciences 2006年第5期23卷 775-783页

作者：姜智娜 State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 Graduate University of the Chinese Academy of Sciences Beijing 100039

A two-layer quasi-geostrophic model is used to study the stability and sensitivity of motions on smallscale vortices in Jupiter＇s atmosphere. Conditional nonlinear optimal perturbations （CNOPs） and linear singular vectors （LSVs） are both obtained numerically and compared in this paper. The results show that CNOPs can capture the nonlinear characteristics of motions in small-scale vortices in Jupiter＇s atmosphere and show great difference from LSVs under the condition that the initial constraint condition is large or the optimization time is not very short or both. Besides, in some basic states, local CNOPs are found. The pattern of LSV is more similar to local CNOP than global CNOP in some cases. The elementary application of the method of CNOP to the Jovian atmosphere helps us to explore the stability of variousscale motions of Jupiter＇s atmosphere and to compare the stability of motions in Jupiter＇s atmosphere and Earth＇s atmosphere further.

关键词： stability sensitivity conditional nonlinear optimal perturbation singular vector

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