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Three-Dimensional Wind Field Retrieved from Dual-Doppler Radar Based on a Variational Method:Refinement of Vertical Velocity Estimates 被引量:1
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作者 Chenbin XUE Zhiying DING +1 位作者 Xinyong SHEN Xian CHEN 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2022年第1期145-160,共16页
In this paper,a scheme of dual-Doppler radar wind analysis based on a three-dimensional variational method is proposed and performed in two steps.First,the horizontal wind field is simultaneously recovered through min... In this paper,a scheme of dual-Doppler radar wind analysis based on a three-dimensional variational method is proposed and performed in two steps.First,the horizontal wind field is simultaneously recovered through minimizing a cost function defined as a radial observation term with the standard conjugate gradient method,avoiding a weighting parameter specification step.Compared with conventional dual-Doppler wind synthesis approaches,this variational method minimizes errors caused by interpolation from radar observation to analysis grid in the iterative solution process,which is one of the main sources of errors.Then,through the accelerated Liebmann method,the vertical velocity is further reestimated as an extra step by solving the Poisson equation with impermeable conditions imposed at the ground and near the tropopause.The Poisson equation defined by the second derivative of the vertical velocity is derived from the mass continuity equation.Compared with the method proposed by O’Brien,this method is less sensitive to the uncertainty of the boundary conditions and has better stability and reliability.Furthermore,the method proposed in this paper is applied to Doppler radar observation of a squall line process.It is shown that the retrieved vertical wind profile agrees well with the vertical profile obtained with the velocity–azimuth display(VAD)method,and the retrieved radial velocity as well as the analyzed positive and negative velocity centers and horizontal wind shear of the squall line are in accord with radar observations.There is a good correspondence between the divergence field of the derived wind field and the vertical velocity.And,the horizontal and vertical circulations within and around the squall line,as well as strong updrafts,the associated downdrafts,and associated rear inflow of the bow echo,are analyzed well.It is worth mentioning that the variational method in this paper can be applied to simultaneously synthesize the three-dimensional wind field from multiple-Doppler radar observations. 展开更多
关键词 dual-Doppler radar three-dimensional wind a variational method vertical velocity wind synthesis
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Multiplicity Results for Second Order Impulsive Differential Equations via Variational Methods 被引量:1
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作者 Huanhuan Wang Dan Lu Huiqin Lu 《Engineering(科研)》 2021年第2期82-93,共12页
In this paper we investigate a class of impulsive differential equations with Dirichlet boundary conditions. Firstly, we define new inner product of <img src="Edit_890fce38-e82b-4f36-be40-9d05e8119b88.png"... In this paper we investigate a class of impulsive differential equations with Dirichlet boundary conditions. Firstly, we define new inner product of <img src="Edit_890fce38-e82b-4f36-be40-9d05e8119b88.png" width="40" height="17" alt="" /> and prove that the norm which is deduced by the inner product is equivalent to the usual norm. Secondly, we construct the lower and upper solutions of (1.1). Thirdly, we obtain the existence of a positive solution, a negative solution and a sign-changing solution by using critical point theory and variational methods. Finally, an example is presented to illustrate the application of our main result. 展开更多
关键词 Impulsive Differential Equation Sign-Changing Solution Critical Point Theory variational method
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Study on Application of Hypervirial Therem in the Variational Method
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作者 DINGYi-Bing LIXue-Qian 《Communications in Theoretical Physics》 SCIE CAS CSCD 2002年第3期283-286,共4页
We discuss a methodology problem which is crucially important for solving the Sch?dinger equation in terms of the variational method. We present a complete analysis on the application of the hypervirial theorem for ju... We discuss a methodology problem which is crucially important for solving the Sch?dinger equation in terms of the variational method. We present a complete analysis on the application of the hypervirial theorem for judging the quality of the trial wavefunction without invoking the precise solutions. 展开更多
关键词 hypervirial theorem variational method linear potential Schrodinger equation
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Research on the discrete variational method for a Birkhoffian system
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作者 刘世兴 花巍 郭永新 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第6期328-332,共5页
In this paper, we present a new integration algorithm based on the discrete Pfaff-Birkhoff principle for Birkhoffian systems. It is proved that the new algorithm can preserve the general symplectic geometric structure... In this paper, we present a new integration algorithm based on the discrete Pfaff-Birkhoff principle for Birkhoffian systems. It is proved that the new algorithm can preserve the general symplectic geometric structures of Birkhoffian systems. A numerical experiment for a damping oscillator system is conducted. The result shows that the new algorithm can better simulate the energy dissipation than the R-K method, which illustrates that we can numerically solve the dynamical equations by the discrete variational method in a Birkhoffian framework for the systems with a general symplectic structure. Furthermore, it is demonstrated that the results of the numerical experiments are determined not by the constructing methods of Birkhoffian functions but by whether the numerical method can preserve the inherent nature of the dynamical system. 展开更多
关键词 Birkhoff's equations discrete variational methods general symplectic structure discrete Birkhoff's equations
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Parameter Estimation with Constraints Based on Variational Method
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作者 施闻明 《Journal of Marine Science and Application》 2010年第1期105-108,共4页
The accuracy of parameter estimation is critical when digitally modeling a ship. A parameter estimation method with constraints was developed, based on the variational method. Performance functions and constraint equa... The accuracy of parameter estimation is critical when digitally modeling a ship. A parameter estimation method with constraints was developed, based on the variational method. Performance functions and constraint equations in the variational method are constructed by analyzing input and output equations of the system. The problem of parameter estimation was transformed into a problem of least squares estimation. The parameter estimation equation was analyzed in order to get an optimized estimation of parameters based on the Lagrange multiplication operator. Simulation results showed that this method is better than the traditional least squares estimation, producing a higher precision when identifying parameters. It has very important practical value in areas of application such as system identification and parameter estimation. 展开更多
关键词 least squares estimation parameter estimation variational method CONSTRAINT
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An analytical variational method for the biased quantum Rabi model in the ultra-strong coupling regime
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作者 Bin-Bin Mao Maoxin Liu +3 位作者 Wei WU Liangsheng Li Zu-Jian Ying Hong-Gang Luo 《Chinese Physics B》 SCIE EI CAS CSCD 2018年第5期322-327,共6页
An analytical variational method for the ground state of the biased quantum Rabi model in the ultra-strong coupling regime is presented. This analytical variational method can be obtained by a unitary transformation o... An analytical variational method for the ground state of the biased quantum Rabi model in the ultra-strong coupling regime is presented. This analytical variational method can be obtained by a unitary transformation or alternatively by assuming the form of the ground state wave function. The key of the method is to introduce a variational parameter λ,which can be determined by minimizing the energy functional. Using this method, we calculate the physical observables with high accuracy in comparison with the numerical exact ones. Our method evidently improves over the widely used general rotating-wave approximation(GRWA) in both qualitative and quantitative aspects. 展开更多
关键词 ultra-strong coupling biased quantum Rabi model analytical variational method
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An efficient parallel algorithm of variational nodal method for heterogeneous neutron transport problems
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作者 Han Yin Xiao-Jing Liu Teng-Fei Zhang 《Nuclear Science and Techniques》 SCIE EI CAS CSCD 2024年第4期29-45,共17页
The heterogeneous variational nodal method(HVNM)has emerged as a potential approach for solving high-fidelity neutron transport problems.However,achieving accurate results with HVNM in large-scale problems using high-... The heterogeneous variational nodal method(HVNM)has emerged as a potential approach for solving high-fidelity neutron transport problems.However,achieving accurate results with HVNM in large-scale problems using high-fidelity models has been challenging due to the prohibitive computational costs.This paper presents an efficient parallel algorithm tailored for HVNM based on the Message Passing Interface standard.The algorithm evenly distributes the response matrix sets among processors during the matrix formation process,thus enabling independent construction without communication.Once the formation tasks are completed,a collective operation merges and shares the matrix sets among the processors.For the solution process,the problem domain is decomposed into subdomains assigned to specific processors,and the red-black Gauss-Seidel iteration is employed within each subdomain to solve the response matrix equation.Point-to-point communication is conducted between adjacent subdomains to exchange data along the boundaries.The accuracy and efficiency of the parallel algorithm are verified using the KAIST and JRR-3 test cases.Numerical results obtained with multiple processors agree well with those obtained from Monte Carlo calculations.The parallelization of HVNM results in eigenvalue errors of 31 pcm/-90 pcm and fission rate RMS errors of 1.22%/0.66%,respectively,for the 3D KAIST problem and the 3D JRR-3 problem.In addition,the parallel algorithm significantly reduces computation time,with an efficiency of 68.51% using 36 processors in the KAIST problem and 77.14% using 144 processors in the JRR-3 problem. 展开更多
关键词 Neutron transport variational nodal method PARALLELIZATION KAIST JRR-3
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A new two-step variational model for multiplicative noise removal with applications to texture images
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作者 ZHANG Long-hui YAO Wen-juan +2 位作者 SHI Sheng-zhu GUO Zhi-chang ZHANG Da-zhi 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第3期486-501,共16页
Multiplicative noise removal problems have attracted much attention in recent years.Unlike additive noise,multiplicative noise destroys almost all information of the original image,especially for texture images.Motiva... Multiplicative noise removal problems have attracted much attention in recent years.Unlike additive noise,multiplicative noise destroys almost all information of the original image,especially for texture images.Motivated by the TV-Stokes model,we propose a new two-step variational model to denoise the texture images corrupted by multiplicative noise with a good geometry explanation in this paper.In the first step,we convert the multiplicative denoising problem into an additive one by the logarithm transform and propagate the isophote directions in the tangential field smoothing.Once the isophote directions are constructed,an image is restored to fit the constructed directions in the second step.The existence and uniqueness of the solution to the variational problems are proved.In these two steps,we use the gradient descent method and construct finite difference schemes to solve the problems.Especially,the augmented Lagrangian method and the fast Fourier transform are adopted to accelerate the calculation.Experimental results show that the proposed model can remove the multiplicative noise efficiently and protect the texture well. 展开更多
关键词 multiplicative noise removal texture images total variation two-step variational method aug-mented Lagrangian method
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Variational Iteration Method for Solving Time Fractional Burgers Equation Using Maple 被引量:1
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作者 Fayza Alwehebi Aatef Hobiny Dalal Maturi 《Applied Mathematics》 2023年第5期336-348,共13页
The Time Fractional Burger equation was solved in this study using the Mabel software and the Variational Iteration approach. where a number of instances of the Time Fractional Burger Equation were handled using this ... The Time Fractional Burger equation was solved in this study using the Mabel software and the Variational Iteration approach. where a number of instances of the Time Fractional Burger Equation were handled using this technique. Tables and images were used to present the collected numerical results. The difference between the exact and numerical solutions demonstrates the effectiveness of the Mabel program’s solution, as well as the accuracy and closeness of the results this method produced. It also demonstrates the Mabel program’s ability to quickly and effectively produce the numerical solution. 展开更多
关键词 variational Iteration method Time Fractional Burgers Equation Maple18
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A Dimension-Splitting Variational Multiscale Element-Free Galerkin Method for Three-Dimensional Singularly Perturbed Convection-Diffusion Problems 被引量:1
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作者 Jufeng Wang Yong Wu +1 位作者 Ying Xu Fengxin Sun 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第4期341-356,共16页
By introducing the dimensional splitting(DS)method into the multiscale interpolating element-free Galerkin(VMIEFG)method,a dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method is propose... By introducing the dimensional splitting(DS)method into the multiscale interpolating element-free Galerkin(VMIEFG)method,a dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method is proposed for three-dimensional(3D)singular perturbed convection-diffusion(SPCD)problems.In the DSVMIEFG method,the 3D problem is decomposed into a series of 2D problems by the DS method,and the discrete equations on the 2D splitting surface are obtained by the VMIEFG method.The improved interpolation-type moving least squares(IIMLS)method is used to construct shape functions in the weak form and to combine 2D discrete equations into a global system of discrete equations for the three-dimensional SPCD problems.The solved numerical example verifies the effectiveness of the method in this paper for the 3D SPCD problems.The numerical solution will gradually converge to the analytical solution with the increase in the number of nodes.For extremely small singular diffusion coefficients,the numerical solution will avoid numerical oscillation and has high computational stability. 展开更多
关键词 Dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method interpolating variational multiscale element-free Galerkin(VMIEFG)method dimension splitting method singularly perturbed convection-diffusion problems
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A Variational Multiscale Method for Particle Dispersion Modeling in the Atmosphere
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作者 Y.Nishio B.Janssens +1 位作者 K.Limam J.van Beeck 《Fluid Dynamics & Materials Processing》 EI 2023年第3期743-753,共11页
A LES model is proposed to predict the dispersion of particles in the atmosphere in the context of Chemical,Biological,Radiological and Nuclear(CBRN)applications.The code relies on the Finite Element Method(FEM)for bo... A LES model is proposed to predict the dispersion of particles in the atmosphere in the context of Chemical,Biological,Radiological and Nuclear(CBRN)applications.The code relies on the Finite Element Method(FEM)for both the fluid and the dispersed solid phases.Starting from the Navier-Stokes equations and a general description of the FEM strategy,the Streamline Upwind Petrov-Galerkin(SUPG)method is formulated putting some emphasis on the related assembly matrix and stabilization coefficients.Then,the Variational Multiscale Method(VMS)is presented together with a detailed illustration of its algorithm and hierarchy of computational steps.It is demonstrated that the VMS can be considered as a more general version of the SUPG method.The final part of the work is used to assess the reliability of the implemented predictor/multicorrector solution strategy. 展开更多
关键词 ABL(Atmospheric boundary layer) CFD FEM LES SUPG(Streamline upwind petrov–Galerkin) Turbulent flow VMS(variational MultiScale method)
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An improved variational method
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作者 曾卓全 沈彭年 丁亦兵 《Chinese Physics C》 SCIE CAS CSCD 2009年第3期191-196,共6页
In order to improve the unitarity of the S-matrix, an improved variational formulism is derived by proposing new generating functionals and adopting proper asymptotic boundary conditions for trial relative wave functi... In order to improve the unitarity of the S-matrix, an improved variational formulism is derived by proposing new generating functionals and adopting proper asymptotic boundary conditions for trial relative wave functions. The formulas with the weighted line-column balance for the single-channel and multi-channel scatterings, where the non-central interaction is implicitly considered, are presented. A numerical check is performed with a soluble model in a four coupled channel scattering problem. The result shows that the high accuracy and the unitarity of the S-matrix are reached. 展开更多
关键词 variational method Galerkin variational method scattering matrix UNITARY
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Variational method based robust adaptive control for a guided spinning rocket 被引量:7
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作者 Zhongjiao Shi Liangyu Zhao Zhijie Liu 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2021年第3期164-175,共12页
In this paper,a robust adaptive controller is designed for a guided spinning rocket,whose dynamics presents the characteristics of pitch-yaw cross coupling,fast time-varying aerodynamics parameters and wide flight env... In this paper,a robust adaptive controller is designed for a guided spinning rocket,whose dynamics presents the characteristics of pitch-yaw cross coupling,fast time-varying aerodynamics parameters and wide flight envelop.First,a coupled nonlinear six-degree-of-freedom equation of motion for a guided spinning rocket is developed,and the lateral acceleration motion is modeled as a control plant with time-varying matched uncertainties and unmodeled dynamics.Then,a robust adaptive control method is proposed by combining Bregman divergence and variational method to achieve fast adaption and maintain bounded tracking.The stability of the resulting closed-loop system is proved,and the ultimate bound and convergence rate are also analyzed.Finally,numerical simulations are performed for a single operating point and the whole flight trajectory to show the robustness and adaptability of the proposed method with respect to timevarying uncertainties and unmodeled dynamics. 展开更多
关键词 Autopilot design Guided spinning rockets Robust adaptive control Second-order adaptive law variational method
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The optimal retrieval of ocean color constituent concentrations based on the variational method 被引量:1
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作者 YU Hong FAN Zhe DU Hua-dong 《Journal of Hydrodynamics》 SCIE EI CSCD 2013年第1期62-71,共10页
In this paper, a new approach to the optimal retrieval of the ocean color based on the variational method is developed by setting up a rational target functional combining with the Broydor Fletcher, Goldfarb, Shanno ... In this paper, a new approach to the optimal retrieval of the ocean color based on the variational method is developed by setting up a rational target functional combining with the Broydor Fletcher, Goldfarb, Shanno (BFGS) optimal algorithm. The numerical tests and the exemplary retrievals are carried out and compared with the statistical retrievals and the optimal retrievals based on the genetic algorithm. The results show that this approach enjoys a higher accuracy as compared to the statistical method and a higher efficiency as compared to the genetic algorithm. The optimal retrieval method presented in this paper provides a new idea for the ocean color inversion and could also be used as a reference for the direct assimilation of the satellite data into the ecological models. 展开更多
关键词 ocean color optimal retrieval variational method Broydor Fletcher Goldfarb Shanno (BFGS) algorithm
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A Variational Method for Estimating Near-Surface Soil Moisture and Surface Heat Fluxes 被引量:1
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作者 张述文 张卫东 邱崇践 《Acta meteorologica Sinica》 SCIE 2007年第4期476-486,共11页
A variational data assimilation method is proposed to estimate the near-surface soil moisture and surface sensible and latent heat fluxes. The method merges the five parts into a cost function, i.e., the differences o... A variational data assimilation method is proposed to estimate the near-surface soil moisture and surface sensible and latent heat fluxes. The method merges the five parts into a cost function, i.e., the differences of wind, potential temperature, and specific humidity gradient between observations and those computed by the profile method, the difference of latent heat fluxes calculated using the ECMWF land surface evaporation scheme and the profile method, and a weak constraint for surface energy balance. By using an optimal algorithm, the best solutions are found. The method is tested with the data collected at Feixi Station (31.41^oN, 117.08^oE) supported by the China Heavy Rain Experiment and Study (HeRES) during 7-30 June 2001. The results show that estimated near-surface soil moistures can quickly respond to rainfall, and their temporal variation is consistent with that of measurements of average soil moisture over 15-cm top depth with a maximum error less than 0.03 m^3 m^-3. The surface heat fluxes calculated by this method are consistent with those by the Bowen ratio method, but at the same time it can overcome the instability problem occurring in the Bowen ratio method when the latter is about -1. Meanwhile, the variational method is more accurate than the profile method in terms of satisfying the surface energy balance. The sensitivity tests also show that the variational method is the most stable one among the three methods. 展开更多
关键词 soil moisture sensible heat flux latent heat flux variational method
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Variational approximation methods for long-range force transmission in biopolymer gels
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作者 Haiqin Wang Xinpeng Xu 《Chinese Physics B》 SCIE EI CAS CSCD 2022年第10期429-435,共7页
The variational principle of minimum free energy(MFEVP) has been widely used in research of soft matter statics.The MFEVP can be used not only to derive equilibrium equations(including both bulk equations and boundary... The variational principle of minimum free energy(MFEVP) has been widely used in research of soft matter statics.The MFEVP can be used not only to derive equilibrium equations(including both bulk equations and boundary conditions),but also to develop direct variational methods(such as Ritz method) to find approximate solutions to these equilibrium equations. We apply these variational methods to study long-range force transmission in nonlinear elastic biopolymer gels.It is shown that the slow decay of cell-induced displacements measured experimentally for fibroblast spheroids in threedimensional fibrin gels can be well explained by variational approximations based on the three-chain model of biopolymer gels. 展开更多
关键词 biopolymer gels cell-cell communications force transmission variational methods
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On the new exact traveling wave solutions of the time-space fractional strain wave equation in microstructured solids via the variational method
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作者 Kang-Jia Wang 《Communications in Theoretical Physics》 SCIE CAS CSCD 2021年第4期1-8,共8页
In this paper,we mainly study the time-space fractional strain wave equation in microstructured solids.He’s variational method,combined with the two-scale transform are implemented to seek the solitary and periodic w... In this paper,we mainly study the time-space fractional strain wave equation in microstructured solids.He’s variational method,combined with the two-scale transform are implemented to seek the solitary and periodic wave solutions of the time-space strain wave equation.The main advantage of the variational method is that it can reduce the order of the differential equation,thus simplifying the equation,making the solving process more intuitive and avoiding the tedious solving process.Finally,the numerical results are shown in the form of 3D and 2D graphs to prove the applicability and effectiveness of the method.The obtained results in this work are expected to shed a bright light on the study of fractional nonlinear partial differential equations in physics. 展开更多
关键词 solitary wave solutions periodic wave solutions fractional strain wave equation variational principle He’s variational method
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APPLICATION OF THE VARIATIONAL METHOD OF TOVS DATA OVER THE TIBETAN PLATEAU IN IMPROVEMENT OF THE INITIAL FIELD OF NUMERICAL MODELS
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作者 翁永辉 徐祥德 +1 位作者 柏晶瑜 董超华 《Acta meteorologica Sinica》 SCIE 2001年第3期362-376,共15页
In this paper,TOVS satellite data are used through variational method on the data-sparse plateau area.Diagnoses are carried out to find a way to solve the large error problem of model initial field.It is put forward t... In this paper,TOVS satellite data are used through variational method on the data-sparse plateau area.Diagnoses are carried out to find a way to solve the large error problem of model initial field.It is put forward that TOVS retrieval data can be used to improve the initial field of numerical prediction model on Tibetan Plateau area.Through variational method,TOVS data are processed and the liability of the initial information on the plateau is improved.Diagnostic results confirm further that the application of TOVS retrieval data can improve our capability to describe the dynamic system features on the plateau and the objectivity of related initial information such as the distribution of water vapor channel and stratification stability. 展开更多
关键词 TOVS retrieval data variational method Tibetan Plateau
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Variational iteration solving method for El Nio phenomenon atmospheric physics of nonlinear model 被引量:14
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作者 MO Jiaqi WANG Hui +1 位作者 LIN Wantao LIN Yihua 《Acta Oceanologica Sinica》 SCIE CAS CSCD 2005年第5期35-38,共4页
A class of E1 Niйo atmospheric physics oscillation model is considered. The E1 Niйo atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmosphere interactions. The conce... A class of E1 Niйo atmospheric physics oscillation model is considered. The E1 Niйo atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmosphere interactions. The conceptual oscillator model should consider the variations of both the eastern and western Pacific anomaly patterns. An E1 Niйo atmospheric physics model is proposed using a method for the variational iteration theory. Using the variational iteration method, the approximate expansions of the solution of corresponding problem are constructed. That is, firstly, introducing a set of functional and accounting their variationals, the Lagrange multiplicators are counted, and then the variational iteration is defined, finally, the approximate solution is obtained. From approximate expansions of the solution, the zonal sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the sea-air oscillation for E1 Niйo atmospheric physics model can be analyzed. E1 Niйo is a very complicated natural phenomenon. Hence basic models need to be reduced for the sea-air oscillator and are solved. The variational iteration is a simple and valid approximate method. 展开更多
关键词 NONLINEAR variational iteration method E1 Niйo phenomenon
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Variational iteration method for solving the mechanism of the Equatorial Eastern Pacific El Nino-Southern Oscillation 被引量:35
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作者 莫嘉祺 王辉 +1 位作者 林万涛 林一骅 《Chinese Physics B》 SCIE EI CAS CSCD 2006年第4期671-675,共5页
A class of coupled system for the E1 Nifio-Southern Oscillation (ENSO) mechanism is studied. Using the method of variational iteration for perturbation theory, the asymptotic expansions of the solution for ENSO mode... A class of coupled system for the E1 Nifio-Southern Oscillation (ENSO) mechanism is studied. Using the method of variational iteration for perturbation theory, the asymptotic expansions of the solution for ENSO model are obtained and the asymptotic behaviour of solution for corresponding problem is considered. 展开更多
关键词 nonlinear method of variational iteration perturbation theory El Nino- Southern Oscillation model
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