A four-dimensional variational （4D-Var） data assimilation method is implemented in an improved intermediate coupled model （ICM） of the tropical Pacific. A twin experiment is designed to evaluate the impact of the ...A four-dimensional variational （4D-Var） data assimilation method is implemented in an improved intermediate coupled model （ICM） of the tropical Pacific. A twin experiment is designed to evaluate the impact of the 4D-Var data assimilation algorithm on ENSO analysis and prediction based on the ICM. The model error is assumed to arise only from the parameter uncertainty. The ＂observation＂ of the SST anomaly, which is sampled from a ＂truth＂ model simulation that takes default parameter values and has Gaussian noise added, is directly assimilated into the assimilation model with its parameters set erroneously. Results show that 4D-Var effectively reduces the error of ENSO analysis and therefore improves the prediction skill of ENSO events compared with the non-assimilation case. These results provide a promising way for the ICM to achieve better real-time ENSO prediction.展开更多
Carbonyls play an important role in the atmospheric chemistry as the main precursor for reactive radicals and peroxyacetyl nitrate.However,little research has been conducted so far on the seasonal variations of carbon...Carbonyls play an important role in the atmospheric chemistry as the main precursor for reactive radicals and peroxyacetyl nitrate.However,little research has been conducted so far on the seasonal variations of carbonyls in China’s urban atmosphere.In this study,ambient carbonyls were 24-hourly observed in four seasons in Hangzhou,a mega-city in the Yangtze River Delta Region,China.The concentration of total carbonyls was the highest in summer(44.35μg/m^(3)),the second in winter(44.05μg/m^(3)),the third in spring(29.31μg/m^(3))and autumn(27.11μg/m^(3)).The most abundant species were found to be acetone in spring,summer,and winter,while formaldehyde in autumn.Rainfall can significantly reduce the concentrations of most ambient carbonyls,with the largest decrease observed in the wet precipitation events occurring in spring and summer,while acetone concentrations remained invariable due to its lower water solubility.Multiple linear regression analysis and carbonyls ratios indicated that anthropogenic emissions were the predominant sources of carbonyls,and atmospheric formaldehyde was mainly emitted from primary sources other than secondary sources.Vehicular exhaust was identified as the primary source of ambient carbonyls,particularly in winter,and its contribution reached 92.80%to formaldehyde.Additionally,photochemical reactions were closely associated with the secondary production of formaldehyde in summer.Carbonyls showed strong ozone formation potential in all four seasons.Based on the health risk assessment,the exposure to ambient carbonyls is harmful to outdoor pedestrians.The results could provide essential information and references for simulating regional air quality and analyzing ozone pollution,which is essential for improving air quality in the Yangtze River Delta region.展开更多
The four-dimensional variational assimilation(4D-Var)has been widely used in meteorological and oceanographic data assimilation.This method is usually implemented in the model space,known as primal approach(P4D-Var).A...The four-dimensional variational assimilation(4D-Var)has been widely used in meteorological and oceanographic data assimilation.This method is usually implemented in the model space,known as primal approach(P4D-Var).Alternatively,physical space analysis system(4D-PSAS)is proposed to reduce the computation cost,in which the 4D-Var problem is solved in physical space(i.e.,observation space).In this study,the conjugate gradient(CG)algorithm,implemented in the 4D-PSAS system is evaluated and it is found that the non-monotonic change of the gradient norm of 4D-PSAS cost function causes artificial oscillations of cost function in the iteration process.The reason of non-monotonic variation of gradient norm in 4D-PSAS is then analyzed.In order to overcome the non-monotonic variation of gradient norm,a new algorithm,Minimum Residual(MINRES)algorithm,is implemented in the process of assimilation iteration in this study.Our experimental results show that the improved 4D-PSAS with the MINRES algorithm guarantees the monotonic reduction of gradient norm of cost function,greatly improves the convergence properties of 4D-PSAS as well,and significantly restrains the numerical noises associated with the traditional 4D-PSAS system.展开更多
The 13-node quadrilateral and 39-node hexahedral cubic serendipity elements produce nodally integrated positive-definite lumped heat capacity matrices in higher-order finite element analysis.However,these elements dis...The 13-node quadrilateral and 39-node hexahedral cubic serendipity elements produce nodally integrated positive-definite lumped heat capacity matrices in higher-order finite element analysis.However,these elements display severe convergence deterioration in explicit transient heat conduction analysis with lumped heat ca-pacity matrices.This convergence decay is due to the violation of variational integration consistency by the standard Galerkin formulation with lumped heat capacity matrices.This issue is resolved by introducing the boundary-enhanced Galerkin weak form that incorporates the elemental boundary contribution in the discrete finite element formulation.Subsequently,it is theoretically proven that a direct nodal integration identically fulfills the variational integration consistency in the context of the boundary-enhanced Galerkin weak form.The proposed variationally consistent nodal integration therefore enables optimal convergence for explicit transient heat conduction analysis with lumped heat capacity matrices.The efficacy of the proposed variationally con-sistent nodal integration formulation for the 13-node quadrilateral and 39-node hexahedral cubic elements is thoroughly demonstrated via numerical examples.展开更多
This study examines the performance of coupling the deterministic four-dimensional variational assimilation system （4DVAR） with an ensemble Kalman filter （EnKF） to produce a superior hybrid approach for data assim...This study examines the performance of coupling the deterministic four-dimensional variational assimilation system （4DVAR） with an ensemble Kalman filter （EnKF） to produce a superior hybrid approach for data assimilation. The coupled assimilation scheme （E4DVAR） benefits from using the state-dependent uncertainty provided by EnKF while taking advantage of 4DVAR in preventing filter divergence： the 4DVAR analysis produces posterior maximum likelihood solutions through minimization of a cost function about which the ensemble perturbations are transformed, and the resulting ensemble analysis can be propagated forward both for the next assimilation cycle and as a basis for ensemble forecasting. The feasibility and effectiveness of this coupled approach are demonstrated in an idealized model with simulated observations. It is found that the E4DVAR is capable of outperforming both 4DVAR and the EnKF under both perfect- and imperfect-model scenarios. The performance of the coupled scheme is also less sensitive to either the ensemble size or the assimilation window length than those for standard EnKF or 4DVAR implementations.展开更多
In practical application, it is very important to master the influence of structure parameters on the mid-span deflection quantificationally. For large-span and heavy-duty gantry cranes, the influence of the rigid leg...In practical application, it is very important to master the influence of structure parameters on the mid-span deflection quantificationally. For large-span and heavy-duty gantry cranes, the influence of the rigid leg and the soft leg on mid-span deflection has not been considered in the past. In the paper, the mathematical model is established for universal large-span and heavy-duty gantry cranes. The analytical solution for the mid-span deflection of gantry-frame structure girder is derived and obtained based on the variation principle by considering the coupling effect of the bending moments of girder and legs, the axial force and the secondary bending moments. The relation between the load and the deflection on the mid-span of the gantry-frame structure girder is known. Then, the experimental model is designed according to dimensional analysis method. And experiments were performed on the WEW-600 B type testing machine. Hackling experimental data, the regular of the load and deflection on the girder mid-span is obtained, namely, the deformation of the gantry-frame structure resists the external load to do work. The validity of the nonlinear analytical solution of the girder deflection is verified. Experimental results show that the analytical solution of the gantry-frame structure deflection has much higher calculation accuracy than previous calculation method. This work provides a theoretical basis for the design and inspection of gantry-frame structures.展开更多
A heavy rainfall event along the mei-yu front during 22-23 June 2002 was chosen for this study. To assess the impact of the routine and additional IOP (intensive observation period) radiosonde observations on the meso...A heavy rainfall event along the mei-yu front during 22-23 June 2002 was chosen for this study. To assess the impact of the routine and additional IOP (intensive observation period) radiosonde observations on the mesoscale heavy rainfall forecast, a series of four-dimensional variational (4DVAR) data assimilation and model simulation experiments was conducted using nonhydrostatic mesoscale model MM5 and the MM5 4DVAR system. The effects of the intensive observations in the different areas on the heavy rainfall forecast were also investigated. The results showed that improvement of the forecast skill for mesoscale heavy rainfall intensity was possible from the assimilation of the IOP radiosonde observations. However, the impact of the IOP observations on the forecast of the rainfall pattern was not significant. Initial conditions obtained through the 4DVAR experiments with a 12-h assimilation window were capable of improving the 24-h forecast. The simulated results after the assimilation showed that it would be best to perform the intensive radiosonde observations in the upstream of the rainfall area and in the moisture passageway area at the same time. Initial conditions created by the 4DVAR led to the low-level moisture convergence over the rainfall area, enhanced frontogenesis and upward motion within the mei-yu front, and intensified middle- and high-level unstable stratification in front of the mei-yu front. Consequently, the heavy rainfall forecast was improved.展开更多
In this paper, variational inference is studied on manifolds with certain metrics. To solve the problem, the analysis is first proposed for the variational Bayesian on Lie group, and then extended to the manifold that...In this paper, variational inference is studied on manifolds with certain metrics. To solve the problem, the analysis is first proposed for the variational Bayesian on Lie group, and then extended to the manifold that is approximated by Lie groups. Then the convergence of the proposed algorithm with respect to the manifold metric is proved in two iterative processes： variational Bayesian expectation （VB-F） step and variational Bayesian maximum （VB-M） step. Moreover, the effective of different metrics for Bayesian analysis is discussed.展开更多
Because they are most sensitive to atmospheric moisture content, radar refractivity observations can provide high-resolution information about the highly variable low-level moisture field. In this study, simulated rad...Because they are most sensitive to atmospheric moisture content, radar refractivity observations can provide high-resolution information about the highly variable low-level moisture field. In this study, simulated radar refractivity-related phase-change data were created using a radar simulator from realistic highresolution model simulation data for a dryline case. These data were analyzed using the 2DVAR system developed specifically for the phase-change data. Two sets of experiments with the simulated observations were performed, one assuming a uniform target spacing of 250 m and one assuming nonuniform spacing between 250 m to 4 km. Several sources of observation error were considered, and their impacts were examined. They included errors due to ground target position uncertainty, typical random errors associated with radar measurements, and gross error due to phase wrapping. Without any additional information, the 2DVAR system was incapable of dealing with phase-wrapped data directly. When there was no phase wrapping in the data, the 2DVAR produced ex- cellent analyses, even in the presence of both position uncertainty and random radar measurement errors. When a separate pre-processing step was applied to unwrap the phase-wrapped data, quality moisture anal- yses were again obtained, although the analyses were smoother due to the reduced effective resolution of the observations by interpolation and smoothing involved in the unwrapping procedure. The unwrapping procedure was effective even when significant differences existed between the analyzed state and the state at a reference time. The results affirm the promise of using radar refractivity phase-change measurements for near-surface moisture analysis.展开更多
A steady-state, rigid-plastic rolling problem for temperature and strain-rate dependent materials with nonlocal friction is considered. A variational formulation is derived, coupling a nonlinear variational inequality...A steady-state, rigid-plastic rolling problem for temperature and strain-rate dependent materials with nonlocal friction is considered. A variational formulation is derived, coupling a nonlinear variational inequality for the velocity and a nonlinear vari- ational equation for the temperature. The existence and uniqueness results are obtained by a proposed fixed point method.展开更多
Tow-phase flow mixed variational formulations of evolution filtration problems with seawater intrusion are analyzed. A dual mixed fractional flow velocity-pressure model is considered with an air-fresh water and a fre...Tow-phase flow mixed variational formulations of evolution filtration problems with seawater intrusion are analyzed. A dual mixed fractional flow velocity-pressure model is considered with an air-fresh water and a fresh water-seawater characterization. For analysis and computational purposes, spatial decompositions based on nonoverlapping multidomains, above and below the sea level, are variationally introduced with internal boundary fluxes dualized as weak transmission constraints. Further, parallel augmented and exactly penalized duality algorithms, and proximation semi-implicit time marching schemes, are established and analyzed.展开更多
On the basis of the general theory of perforated thin plates under large deflections, variational principles with deflection w and stress function F as variables are stated in detail.Based on these princi- ples,finite...On the basis of the general theory of perforated thin plates under large deflections, variational principles with deflection w and stress function F as variables are stated in detail.Based on these princi- ples,finite element method is established for analysing the buckling and post-buckling of perforated thin plates. It is found that the property of element is very complicated,owing to the multiple connexity of the region.展开更多
On foe basis of the Kirchoff-Karman hypothses for the nonlinear bending of thin plates, the three kinds of boundary value problems of nonlinear analysis for perforated fhin plates are presented under the differenr in...On foe basis of the Kirchoff-Karman hypothses for the nonlinear bending of thin plates, the three kinds of boundary value problems of nonlinear analysis for perforated fhin plates are presented under the differenr in-plane boundary conditions and the corresponding generalized varialional principles are established. One can see that all mathematical models presented in this paper are completely new ones and differ from the ordinary von Karman theory. These mathematical models can be applied to the nonlinear analysis and the Stability analysis of perforaled thin plates in arbitraryplane boundary conditions.展开更多
Accurate forecast of rainstorms associated with the mei-yu front has been an important issue for the Chinese economy and society. In July 1998 a heavy rainstorm hit the Yangzi River valley and received widespread atte...Accurate forecast of rainstorms associated with the mei-yu front has been an important issue for the Chinese economy and society. In July 1998 a heavy rainstorm hit the Yangzi River valley and received widespread attention from the public because it caused catastrophic damage in China. Several numerical studies have shown that many forecast models, including Pennsylvania State University National Center for Atmospheric Research’s fifth-generation mesoscale model （MM5）, failed to simulate the heavy precipitation over the Yangzi River valley. This study demonstrates that with the optimal initial conditions from the dimension-reduced projection four-dimensional variational data assimilation （DRP-4DVar） system, MM5 can successfully reproduce these observed rainfall amounts and can capture many important mesoscale features, including the southwestward shear line and the low-level jet stream. The study also indicates that the failure of previous forecasts can be mainly attributed to the lack of mesoscale details in the initial conditions of the models.展开更多
Forecasting convective storms using NWP models is an important goal and a highly active area of ongoing research. Skillful and reliable NWP of convective storms could allow for severe weather warnings with longer lead...Forecasting convective storms using NWP models is an important goal and a highly active area of ongoing research. Skillful and reliable NWP of convective storms could allow for severe weather warnings with longer lead times, as opera- tional forecasters begin to incorporate convective-scale fore- casts into severe weather forecast operations （Stensrud et al., 2009, 2013）. This would then provide vulnerable individuals and industries with more time to seek shelter and/or mitigate the impact of severe weather hazards.展开更多
The generalized method of variational analysis (GMVA) suggested for 2-D wind observations by Huang et al. is extended to 3-D cases. Just as in 2-D cases, the regularization idea is applied. But due to the complexity...The generalized method of variational analysis (GMVA) suggested for 2-D wind observations by Huang et al. is extended to 3-D cases. Just as in 2-D cases, the regularization idea is applied. But due to the complexity of the 3-D cases, the vertical vorticity is taken as a stable functional. The results indicate that wind observations can be both variationally optimized and ?ltered. The e?ciency of GMVA is also checked in a numerical test. Finally, 3-D wind observations with random disturbances are manipulated by GMVA after being ?ltered.展开更多
In this paper, a set of variational formulas of solving nonlinear instability critical loads are established from the viewpoint of variational principle. The paper shows that it is very convenient to solve nonlinear i...In this paper, a set of variational formulas of solving nonlinear instability critical loads are established from the viewpoint of variational principle. The paper shows that it is very convenient to solve nonlinear instability critical load by using the variational formulas suggested in this paper.展开更多
This paper extends the quantitative stability results to a more general class of two-stage stochastic variational inequality problems(TSVIP).The existence of solutions to the TSVIP is discussed,and the quantitative re...This paper extends the quantitative stability results to a more general class of two-stage stochastic variational inequality problems(TSVIP).The existence of solutions to the TSVIP is discussed,and the quantitative relationship between the TSVIP and its distribution perturbed problem is derived.展开更多
A mixed vuriational formulation for large deformation analysis of plates is introduced. In this formulation the equilibrium ami compatibility equations are satisfied identically by means of stress functions and displa...A mixed vuriational formulation for large deformation analysis of plates is introduced. In this formulation the equilibrium ami compatibility equations are satisfied identically by means of stress functions and displacement components, respectively, and the constitu,lye equations are satisfied in a least square sense. An example is solved and the results are compared with those available in the literature.Further, the functional is particularized for buckling analysis of plates and a simple example is solved to illustrate the theory.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.41490644,41475101 and 41421005)the CAS Strategic Priority Project(the Western Pacific Ocean System+2 种基金Project Nos.XDA11010105,XDA11020306 and XDA11010301)the NSFC-Shandong Joint Fund for Marine Science Research Centers(Grant No.U1406401)the NSFC Innovative Group Grant(Project No.41421005)
文摘A four-dimensional variational （4D-Var） data assimilation method is implemented in an improved intermediate coupled model （ICM） of the tropical Pacific. A twin experiment is designed to evaluate the impact of the 4D-Var data assimilation algorithm on ENSO analysis and prediction based on the ICM. The model error is assumed to arise only from the parameter uncertainty. The ＂observation＂ of the SST anomaly, which is sampled from a ＂truth＂ model simulation that takes default parameter values and has Gaussian noise added, is directly assimilated into the assimilation model with its parameters set erroneously. Results show that 4D-Var effectively reduces the error of ENSO analysis and therefore improves the prediction skill of ENSO events compared with the non-assimilation case. These results provide a promising way for the ICM to achieve better real-time ENSO prediction.
基金supported by the National Natural Science Founda-tion of China(Nos.42327806 and 52370108)Zhejiang Provincial Leading Project for Leading Geese Plan(No.2025C03073).
文摘Carbonyls play an important role in the atmospheric chemistry as the main precursor for reactive radicals and peroxyacetyl nitrate.However,little research has been conducted so far on the seasonal variations of carbonyls in China’s urban atmosphere.In this study,ambient carbonyls were 24-hourly observed in four seasons in Hangzhou,a mega-city in the Yangtze River Delta Region,China.The concentration of total carbonyls was the highest in summer(44.35μg/m^(3)),the second in winter(44.05μg/m^(3)),the third in spring(29.31μg/m^(3))and autumn(27.11μg/m^(3)).The most abundant species were found to be acetone in spring,summer,and winter,while formaldehyde in autumn.Rainfall can significantly reduce the concentrations of most ambient carbonyls,with the largest decrease observed in the wet precipitation events occurring in spring and summer,while acetone concentrations remained invariable due to its lower water solubility.Multiple linear regression analysis and carbonyls ratios indicated that anthropogenic emissions were the predominant sources of carbonyls,and atmospheric formaldehyde was mainly emitted from primary sources other than secondary sources.Vehicular exhaust was identified as the primary source of ambient carbonyls,particularly in winter,and its contribution reached 92.80%to formaldehyde.Additionally,photochemical reactions were closely associated with the secondary production of formaldehyde in summer.Carbonyls showed strong ozone formation potential in all four seasons.Based on the health risk assessment,the exposure to ambient carbonyls is harmful to outdoor pedestrians.The results could provide essential information and references for simulating regional air quality and analyzing ozone pollution,which is essential for improving air quality in the Yangtze River Delta region.
基金The National Key Research and Development Program of China under contract Nos 2017YFC1501803 and2018YFC1506903the National Natural Science Foundation of China under contract Nos 91730304,41475021 and 41575026
文摘The four-dimensional variational assimilation(4D-Var)has been widely used in meteorological and oceanographic data assimilation.This method is usually implemented in the model space,known as primal approach(P4D-Var).Alternatively,physical space analysis system(4D-PSAS)is proposed to reduce the computation cost,in which the 4D-Var problem is solved in physical space(i.e.,observation space).In this study,the conjugate gradient(CG)algorithm,implemented in the 4D-PSAS system is evaluated and it is found that the non-monotonic change of the gradient norm of 4D-PSAS cost function causes artificial oscillations of cost function in the iteration process.The reason of non-monotonic variation of gradient norm in 4D-PSAS is then analyzed.In order to overcome the non-monotonic variation of gradient norm,a new algorithm,Minimum Residual(MINRES)algorithm,is implemented in the process of assimilation iteration in this study.Our experimental results show that the improved 4D-PSAS with the MINRES algorithm guarantees the monotonic reduction of gradient norm of cost function,greatly improves the convergence properties of 4D-PSAS as well,and significantly restrains the numerical noises associated with the traditional 4D-PSAS system.
基金supported by the National Natural Science Foundation of China(Grant Nos.12372201 and 12072302).
文摘The 13-node quadrilateral and 39-node hexahedral cubic serendipity elements produce nodally integrated positive-definite lumped heat capacity matrices in higher-order finite element analysis.However,these elements display severe convergence deterioration in explicit transient heat conduction analysis with lumped heat ca-pacity matrices.This convergence decay is due to the violation of variational integration consistency by the standard Galerkin formulation with lumped heat capacity matrices.This issue is resolved by introducing the boundary-enhanced Galerkin weak form that incorporates the elemental boundary contribution in the discrete finite element formulation.Subsequently,it is theoretically proven that a direct nodal integration identically fulfills the variational integration consistency in the context of the boundary-enhanced Galerkin weak form.The proposed variationally consistent nodal integration therefore enables optimal convergence for explicit transient heat conduction analysis with lumped heat capacity matrices.The efficacy of the proposed variationally con-sistent nodal integration formulation for the 13-node quadrilateral and 39-node hexahedral cubic elements is thoroughly demonstrated via numerical examples.
基金sponsored by the U.S. National Science Foundation (Grant No.ATM0205599)the U.S. Offce of Navy Research under Grant N000140410471Dr. James A. Hansen was partially supported by US Offce of Naval Research (Grant No. N00014-06-1-0500)
文摘This study examines the performance of coupling the deterministic four-dimensional variational assimilation system （4DVAR） with an ensemble Kalman filter （EnKF） to produce a superior hybrid approach for data assimilation. The coupled assimilation scheme （E4DVAR） benefits from using the state-dependent uncertainty provided by EnKF while taking advantage of 4DVAR in preventing filter divergence： the 4DVAR analysis produces posterior maximum likelihood solutions through minimization of a cost function about which the ensemble perturbations are transformed, and the resulting ensemble analysis can be propagated forward both for the next assimilation cycle and as a basis for ensemble forecasting. The feasibility and effectiveness of this coupled approach are demonstrated in an idealized model with simulated observations. It is found that the E4DVAR is capable of outperforming both 4DVAR and the EnKF under both perfect- and imperfect-model scenarios. The performance of the coupled scheme is also less sensitive to either the ensemble size or the assimilation window length than those for standard EnKF or 4DVAR implementations.
基金Project(51175442)supported by the National Natural Science Foundation of ChinaProject(QD2012A09)supported by Teachers’College Research Project,ChinaProject(14ZA0263)supported by Research Project of Sichuan Provincial Department of Education,China
文摘In practical application, it is very important to master the influence of structure parameters on the mid-span deflection quantificationally. For large-span and heavy-duty gantry cranes, the influence of the rigid leg and the soft leg on mid-span deflection has not been considered in the past. In the paper, the mathematical model is established for universal large-span and heavy-duty gantry cranes. The analytical solution for the mid-span deflection of gantry-frame structure girder is derived and obtained based on the variation principle by considering the coupling effect of the bending moments of girder and legs, the axial force and the secondary bending moments. The relation between the load and the deflection on the mid-span of the gantry-frame structure girder is known. Then, the experimental model is designed according to dimensional analysis method. And experiments were performed on the WEW-600 B type testing machine. Hackling experimental data, the regular of the load and deflection on the girder mid-span is obtained, namely, the deformation of the gantry-frame structure resists the external load to do work. The validity of the nonlinear analytical solution of the girder deflection is verified. Experimental results show that the analytical solution of the gantry-frame structure deflection has much higher calculation accuracy than previous calculation method. This work provides a theoretical basis for the design and inspection of gantry-frame structures.
文摘A heavy rainfall event along the mei-yu front during 22-23 June 2002 was chosen for this study. To assess the impact of the routine and additional IOP (intensive observation period) radiosonde observations on the mesoscale heavy rainfall forecast, a series of four-dimensional variational (4DVAR) data assimilation and model simulation experiments was conducted using nonhydrostatic mesoscale model MM5 and the MM5 4DVAR system. The effects of the intensive observations in the different areas on the heavy rainfall forecast were also investigated. The results showed that improvement of the forecast skill for mesoscale heavy rainfall intensity was possible from the assimilation of the IOP radiosonde observations. However, the impact of the IOP observations on the forecast of the rainfall pattern was not significant. Initial conditions obtained through the 4DVAR experiments with a 12-h assimilation window were capable of improving the 24-h forecast. The simulated results after the assimilation showed that it would be best to perform the intensive radiosonde observations in the upstream of the rainfall area and in the moisture passageway area at the same time. Initial conditions created by the 4DVAR led to the low-level moisture convergence over the rainfall area, enhanced frontogenesis and upward motion within the mei-yu front, and intensified middle- and high-level unstable stratification in front of the mei-yu front. Consequently, the heavy rainfall forecast was improved.
基金This work was supported by the National Key Research and Development Program of China （No. 2016YF-B0901900） and the National Natural Science Foundation of China （Nos. 61733018, 61333001, 61573344）.
文摘In this paper, variational inference is studied on manifolds with certain metrics. To solve the problem, the analysis is first proposed for the variational Bayesian on Lie group, and then extended to the manifold that is approximated by Lie groups. Then the convergence of the proposed algorithm with respect to the manifold metric is proved in two iterative processes： variational Bayesian expectation （VB-F） step and variational Bayesian maximum （VB-M） step. Moreover, the effective of different metrics for Bayesian analysis is discussed.
基金supported by the National Science Foundation (Grant No. AGS-0750790)supported by the NSF grants (Grant Nos. AGS-0802888,OCI-0905040,AGS-0941491,AGS-1046171,and AGS-1046081)
文摘Because they are most sensitive to atmospheric moisture content, radar refractivity observations can provide high-resolution information about the highly variable low-level moisture field. In this study, simulated radar refractivity-related phase-change data were created using a radar simulator from realistic highresolution model simulation data for a dryline case. These data were analyzed using the 2DVAR system developed specifically for the phase-change data. Two sets of experiments with the simulated observations were performed, one assuming a uniform target spacing of 250 m and one assuming nonuniform spacing between 250 m to 4 km. Several sources of observation error were considered, and their impacts were examined. They included errors due to ground target position uncertainty, typical random errors associated with radar measurements, and gross error due to phase wrapping. Without any additional information, the 2DVAR system was incapable of dealing with phase-wrapped data directly. When there was no phase wrapping in the data, the 2DVAR produced ex- cellent analyses, even in the presence of both position uncertainty and random radar measurement errors. When a separate pre-processing step was applied to unwrap the phase-wrapped data, quality moisture anal- yses were again obtained, although the analyses were smoother due to the reduced effective resolution of the observations by interpolation and smoothing involved in the unwrapping procedure. The unwrapping procedure was effective even when significant differences existed between the analyzed state and the state at a reference time. The results affirm the promise of using radar refractivity phase-change measurements for near-surface moisture analysis.
文摘A steady-state, rigid-plastic rolling problem for temperature and strain-rate dependent materials with nonlocal friction is considered. A variational formulation is derived, coupling a nonlinear variational inequality for the velocity and a nonlinear vari- ational equation for the temperature. The existence and uniqueness results are obtained by a proposed fixed point method.
文摘Tow-phase flow mixed variational formulations of evolution filtration problems with seawater intrusion are analyzed. A dual mixed fractional flow velocity-pressure model is considered with an air-fresh water and a fresh water-seawater characterization. For analysis and computational purposes, spatial decompositions based on nonoverlapping multidomains, above and below the sea level, are variationally introduced with internal boundary fluxes dualized as weak transmission constraints. Further, parallel augmented and exactly penalized duality algorithms, and proximation semi-implicit time marching schemes, are established and analyzed.
基金Project supported by National Natural Science Foundation of China.
文摘On the basis of the general theory of perforated thin plates under large deflections, variational principles with deflection w and stress function F as variables are stated in detail.Based on these princi- ples,finite element method is established for analysing the buckling and post-buckling of perforated thin plates. It is found that the property of element is very complicated,owing to the multiple connexity of the region.
文摘On foe basis of the Kirchoff-Karman hypothses for the nonlinear bending of thin plates, the three kinds of boundary value problems of nonlinear analysis for perforated fhin plates are presented under the differenr in-plane boundary conditions and the corresponding generalized varialional principles are established. One can see that all mathematical models presented in this paper are completely new ones and differ from the ordinary von Karman theory. These mathematical models can be applied to the nonlinear analysis and the Stability analysis of perforaled thin plates in arbitraryplane boundary conditions.
基金the National Basic Research Program (973 Program) (No.2010CB 951604)the China Meteorological Administration for the R&D Special Fund for Public Welfare Industry (meteorology) [Grant No. GYHY(QX)200906009]+1 种基金the National High Technology Research and Development Program of China (863 Program) (No. 2010AA012304)the LASG free exploration fund
文摘Accurate forecast of rainstorms associated with the mei-yu front has been an important issue for the Chinese economy and society. In July 1998 a heavy rainstorm hit the Yangzi River valley and received widespread attention from the public because it caused catastrophic damage in China. Several numerical studies have shown that many forecast models, including Pennsylvania State University National Center for Atmospheric Research’s fifth-generation mesoscale model （MM5）, failed to simulate the heavy precipitation over the Yangzi River valley. This study demonstrates that with the optimal initial conditions from the dimension-reduced projection four-dimensional variational data assimilation （DRP-4DVar） system, MM5 can successfully reproduce these observed rainfall amounts and can capture many important mesoscale features, including the southwestward shear line and the low-level jet stream. The study also indicates that the failure of previous forecasts can be mainly attributed to the lack of mesoscale details in the initial conditions of the models.
文摘Forecasting convective storms using NWP models is an important goal and a highly active area of ongoing research. Skillful and reliable NWP of convective storms could allow for severe weather warnings with longer lead times, as opera- tional forecasters begin to incorporate convective-scale fore- casts into severe weather forecast operations （Stensrud et al., 2009, 2013）. This would then provide vulnerable individuals and industries with more time to seek shelter and/or mitigate the impact of severe weather hazards.
基金the National Natural Science Foundation of China(No.40075014,40175014)Shanghai Science and Technology Association(No.02DJ14032).
文摘The generalized method of variational analysis (GMVA) suggested for 2-D wind observations by Huang et al. is extended to 3-D cases. Just as in 2-D cases, the regularization idea is applied. But due to the complexity of the 3-D cases, the vertical vorticity is taken as a stable functional. The results indicate that wind observations can be both variationally optimized and ?ltered. The e?ciency of GMVA is also checked in a numerical test. Finally, 3-D wind observations with random disturbances are manipulated by GMVA after being ?ltered.
文摘In this paper, a set of variational formulas of solving nonlinear instability critical loads are established from the viewpoint of variational principle. The paper shows that it is very convenient to solve nonlinear instability critical load by using the variational formulas suggested in this paper.
基金Supported by the Guangxi Natural Science Foundation (2024GXNSFBA010345)the Innovation and Entrepreneurship Training Program of Guangxi Minzu University (S202310608001)。
文摘This paper extends the quantitative stability results to a more general class of two-stage stochastic variational inequality problems(TSVIP).The existence of solutions to the TSVIP is discussed,and the quantitative relationship between the TSVIP and its distribution perturbed problem is derived.
文摘A mixed vuriational formulation for large deformation analysis of plates is introduced. In this formulation the equilibrium ami compatibility equations are satisfied identically by means of stress functions and displacement components, respectively, and the constitu,lye equations are satisfied in a least square sense. An example is solved and the results are compared with those available in the literature.Further, the functional is particularized for buckling analysis of plates and a simple example is solved to illustrate the theory.
