Accurately simulating mesoscale convective systems(MCSs)is essential for predicting global precipitation patterns and extreme weather events.Despite the ability of advanced models to reproduce MCS climate statistics,c...Accurately simulating mesoscale convective systems(MCSs)is essential for predicting global precipitation patterns and extreme weather events.Despite the ability of advanced models to reproduce MCS climate statistics,capturing extreme storm cases over complex terrain remains challenging.This study utilizes the Global–Regional Integrated Forecast System(GRIST)with variable resolution to simulate an eastward-propagating MCS event.The impact of three microphysics schemes,including two single-moment schemes(WSM6,Lin)and one double-moment scheme(Morrison),on the model sensitivity of MCS precipitation simulations is investigated.The results demonstrate that while all the schemes capture the spatial distribution and temporal variation of MCS precipitation,the Morrison scheme alleviates overestimated precipitation compared to the Lin and WSM6 schemes.The ascending motion gradually becomes weaker in the Morrison scheme during the MCS movement process.Compared to the runs with convection parameterization,the explicit-convection setup at 3.5-km resolution reduces disparities in atmospheric dynamics due to microphysics sensitivity in terms of vertical motions and horizontal kinetic energy at the high-wavenumber regimes.The explicit-convection setup more accurately captures the propagation of both main and secondary precipitation centers during the MCS development,diminishing the differences in both precipitation intensity and propagation features between the Morrison and two single-moment schemes.These findings underscore the importance of microphysics schemes for global nonhydrostatic modeling at the kilometer scale.The role of explicit convection for reducing model uncertainty is also outlined.展开更多
Here,a nonhydrostatic alternative scheme(NAS)is proposed for the grey zone where the nonhydrostatic impact on the atmosphere is evident but not large enough to justify the necessity to include an implicit nonhydrostat...Here,a nonhydrostatic alternative scheme(NAS)is proposed for the grey zone where the nonhydrostatic impact on the atmosphere is evident but not large enough to justify the necessity to include an implicit nonhydrostatic solver in an atmospheric dynamical core.The NAS is designed to replace this solver,which can be incorporated into any hydrostatic models so that existing well-developed hydrostatic models can effectively serve for a longer time.Recent advances in machine learning(ML)provide a potential tool for capturing the main complicated nonlinear-nonhydrostatic relationship.In this study,an ML approach called a neural network(NN)was adopted to select leading input features and develop the NAS.The NNs were trained and evaluated with 12-day simulation results of dry baroclinic-wave tests by the Weather Research and Forecasting(WRF)model.The forward time difference of the nonhydrostatic tendency was used as the target variable,and the five selected features were the nonhydrostatic tendency at the last time step,and four hydrostatic variables at the current step including geopotential height,pressure in two different forms,and potential temperature,respectively.Finally,a practical NAS was developed with these features and trained layer by layer at a 20-km horizontal resolution,which can accurately reproduce the temporal variation and vertical distribution of the nonhydrostatic tendency.Corrected by the NN-based NAS,the improved hydrostatic solver at different horizontal resolutions can run stably for at least one month and effectively reduce most of the nonhydrostatic errors in terms of system bias,anomaly root-mean-square error,and the error of the wave spatial pattern,which proves the feasibility and superiority of this scheme.展开更多
The equations of state(EOSs)of materials are the cornerstone of condensed matter physics,material science,and geophysics.However,acquiring an accurate EOS in diamond anvil cell(DAC)experiments continues to prove probl...The equations of state(EOSs)of materials are the cornerstone of condensed matter physics,material science,and geophysics.However,acquiring an accurate EOS in diamond anvil cell(DAC)experiments continues to prove problematic because the current lack of an accurate pressure scale with clarified sources of uncertainty makes it difficult to determine a precise pressure value at high pressure,and nonhydrostaticity affects both the volume and pressure determination.This study will discuss the advantages and drawbacks of various pressure scales,and propose an absolute pressure scale and correction methods for the effects of non-hydrostaticity.At the end of this paper,we analyze the accuracy of the determined EOS in the DAC experiments we can achieve to date.展开更多
A 3D dynamic core of the non-hydrostatic model GRAPES（Global/Regional Assimilation and Prediction System） is developed on the Yin-Yang grid to address the polar problem and to enhance the computational efficiency. T...A 3D dynamic core of the non-hydrostatic model GRAPES（Global/Regional Assimilation and Prediction System） is developed on the Yin-Yang grid to address the polar problem and to enhance the computational efficiency. Three-dimensional Coriolis forcing is introduced to the new core, and full representation of the Coriolis forcing makes it straightforward to share code between the Yin and Yang subdomains. Similar to that in the original GRAPES model, a semi-implicit semi-Lagrangian scheme is adopted for temporal integration and advection with additional arrangement for cross-boundary transport. Under a non-centered second-order temporal and spatial discretization, the dry nonhydrostatic frame is summarized as the solution of an elliptical problem. The resulting Helmholtz equation is solved with the Generalized Conjugate Residual solver in cooperation with the classic Schwarz method. Even though the coefficients of the equation are quite different from those in the original model, the computational procedure of the new core is just the same. The bi-cubic Lagrangian interpolation serves to provide Dirichlet-type boundary conditions with data transfer between the subdomains. The dry core is evaluated with several benchmark test cases, and all the tests display reasonable numerical stability and computing performance. Persistency of the balanced flow and development of both the mountain-induced Rossby wave and Rossby–Haurwitz wave confirms the appropriate installation of the 3D Coriolis terms in the semi-implicit semi-Lagrangian dynamic core on the Yin-Yang grid.展开更多
A 3D compressible nonhydrostatic dynamic core based on a three-point multi-moment constrained finite-volume (MCV) method is developed by extending the previous 2D nonhydrostatic atmospheric dynamics to 3D on a terrain...A 3D compressible nonhydrostatic dynamic core based on a three-point multi-moment constrained finite-volume (MCV) method is developed by extending the previous 2D nonhydrostatic atmospheric dynamics to 3D on a terrainfollowing grid. The MCV algorithm defines two types of moments: the point-wise value (PV) and the volume-integrated average (VIA). The unknowns (PV values) are defined at the solution points within each cell and are updated through the time evolution formulations derived from the governing equations. Rigorous numerical conservation is ensured by a constraint on the VIA moment through the flux form formulation. The 3D atmospheric dynamic core reported in this paper is based on a three-point MCV method and has some advantages in comparison with other existing methods, such as uniform third-order accuracy, a compact stencil, and algorithmic simplicity. To check the performance of the 3D nonhydrostatic dynamic core, various benchmark test cases are performed. All the numerical results show that the present dynamic core is very competitive when compared to other existing advanced models, and thus lays the foundation for further developing global atmospheric models in the near future.展开更多
A nonhydrostatic numerical model was developed and numerical experiments performed on the interaction of an internal solitary wave （ISW） with a sill, for a two-layer fluid with a diffusive interface. Based on the bl...A nonhydrostatic numerical model was developed and numerical experiments performed on the interaction of an internal solitary wave （ISW） with a sill, for a two-layer fluid with a diffusive interface. Based on the blocking parameter （Br）, the flow was classified into three cases： （1） when bottom topography has little influence on the propagation and spatial structure of the ISW （Br〈0.5）, （2） where the ISW is distorted significantly by the blocking effect of the topography （though no wave breaking occurs, （0.5〈Br〈0.7）, and （3） where the ISW is broken as it encounters and passes over the bottom topography （0.7〈Br）. The numerical results obtained here are consistent with those obtained in laboratory experiments. The breaking process of the incident ISW when Br=0.7 was completely reproduced. Dissipation rate was linearly related to the blocking parameter when B,〈0.7, and the maximum dissipation rate could reach about 34% as Br raised to about 1.0. After that, instead of breaking, more reflection happened. Similarly, breaking induced mixing was also most effective during Br around 1.0, and can be up to 0.16.展开更多
A high resolution nonhydrostatic tropical atmospheric model is developed by using a ready-made regional atmospheric modeling system. The motivation is to investigate the convective activities associated with the tropi...A high resolution nonhydrostatic tropical atmospheric model is developed by using a ready-made regional atmospheric modeling system. The motivation is to investigate the convective activities associated with the tropical intraseasonal oscillation (ISO) through a cloud resolving calculation. Due to limitations in computing resources, a展开更多
With the development of numerical weather prediction technology, the traditional global hydrostatic models used in many countries of the world for operational weather forecasting and numerical simulations of general c...With the development of numerical weather prediction technology, the traditional global hydrostatic models used in many countries of the world for operational weather forecasting and numerical simulations of general circulation have become more and more unfit for high-impact weather prediction. To address this, it is important to invest in the development of global nonhydrostatic models. Few existing nonhydrostatic global models use consistently the grid finite difference scheme for the primitive equations of dynamical cores, which can subsequently degrade the accuracy of the calculations. A new nonhydrostatic global spectral model, which utilizes the Eulerian spectral method, is developed here from NCAR Community Atmosphere Model 3.0 （CAM3.0）. Using Janjic＇s hydrostatic/nonhydrostatic method, a global nonhydrostatic spectral method for the primitive equations has been formulated and developed. In order to retain the integrity of the nonhydrostatic equations, the atmospheric curvature correction and eccentricity correction are considered. In this paper, the Held-Suarez idealized test and an idealized baroclinic wave test are first carried out, which shows that the nonhydrostatic global spectral model has similar climate states to the results of many other global models for long-term idealized integration, as well as better simulation ability for short-term idealized integration. Then, a real case experiment is conducted using the new dynamical core with the full physical parameterizations of subgrid-scale physical processes. The 10-day numerical integration indicates a decrease in systematic error and a better simulation of zonal wind, temperature, and 500-hPa height.展开更多
Nonlinear internal waves(NIWs) are ubiquitous around the Kara Sea, a part of the Arctic Ocean that is north of Siberia. Three hot spot sources for internal waves, one of which is the Kara Strait, have been identified ...Nonlinear internal waves(NIWs) are ubiquitous around the Kara Sea, a part of the Arctic Ocean that is north of Siberia. Three hot spot sources for internal waves, one of which is the Kara Strait, have been identified based on Envisat ASAR. The generation and evolution of the NIWs through the interactions of the tide and topography across the strait is studied based on a nonhydrostatic numerical model. The model captures most wave characteristics shown by satellite data. A typical inter-packets distance on the Barents Sea side is about 25 km in summer, with a phase speed about 0.65 m/s. A northward background current may intensify the accumulation of energy during generation, but it has little influence on the other properties of the generated waves. The single internal solitary wave(ISW) structure is a special phenomenon that follows major wave trains, with a distance about 5–8 km. This wave is generated with the leading wave packets during the same tidal period. When a steady current toward the Kara Sea is included, the basic generation process is similar, but the waves toward the Kara Sea weaken and display an internal bore-like structure with smaller amplitude than in the control experiment. In winter, due to the growth of sea ice, stratification across the Kara Strait is mainly determined by the salinity, with an almost uniform temperature close to freezing. A pycnocline deepens near the middle of the water depth(Barents Sea side), and the NIWs process is not as important as the NIWs process in summer. There is no fission process during the simulation.展开更多
A high resolution, nonhydrostatic, three dimensional diagnostic PBL model over small scale concave terrain was established in this paper. A two dimensional prognostic model was developed based on the diagnostic mo...A high resolution, nonhydrostatic, three dimensional diagnostic PBL model over small scale concave terrain was established in this paper. A two dimensional prognostic model was developed based on the diagnostic model. The hydrostatic approximation was abandoned and the simple energy ( E e ) closure scheme was used in both models. Using the two models, characteristics of PBL structure and its evolution were fully studied. The main characteristic of the PBL is the circulation, and it fairly affects the distribution of the pollutant in the pit.展开更多
The potential temperature vorticity has been introduced to polish the (momentum) vorticity - streamfunction method for solving the two-dimensional and nonhydrostatic model with much accuracy but not many increments of...The potential temperature vorticity has been introduced to polish the (momentum) vorticity - streamfunction method for solving the two-dimensional and nonhydrostatic model with much accuracy but not many increments of computation. The three-step procedure introduced in the present paper can be used to solve both shallow and deep dynamic models.展开更多
An adaptive 2 D nonhydrostatic dynamical core is proposed by using the multi-moment constrained finite-volume(MCV) scheme and the Berger-Oliger adaptive mesh refinement(AMR) algorithm. The MCV scheme takes several poi...An adaptive 2 D nonhydrostatic dynamical core is proposed by using the multi-moment constrained finite-volume(MCV) scheme and the Berger-Oliger adaptive mesh refinement(AMR) algorithm. The MCV scheme takes several pointwise values within each computational cell as the predicted variables to build high-order schemes based on single-cell reconstruction. Two types of moments, such as the volume-integrated average(VIA) and point value(PV), are defined as constraint conditions to derive the updating formulations of the unknowns, and the constraint condition on VIA guarantees the rigorous conservation of the proposed model. In this study, the MCV scheme is implemented on a height-based, terrainfollowing grid with variable resolution to solve the nonhydrostatic governing equations of atmospheric dynamics. The AMR grid of Berger-Oliger consists of several groups of blocks with different resolutions, where the MCV model developed on a fixed structured mesh can be used directly. Numerical formulations are designed to implement the coarsefine interpolation and the flux correction for properly exchanging the solution information among different blocks. Widely used benchmark tests are carried out to evaluate the proposed model. The numerical experiments on uniform and AMR grids indicate that the adaptive model has promising potential for improving computational efficiency without losing accuracy.展开更多
Forecasts and simulations are varied owing to different allocation of 3-dimensional variables in mesoscale models. No attempts have been made to address the issue of optimizing the simulation with a 3-dimensional vari...Forecasts and simulations are varied owing to different allocation of 3-dimensional variables in mesoscale models. No attempts have been made to address the issue of optimizing the simulation with a 3-dimensional variables distribution that should come to be. On the basis of linear nonhydrostatic anelastic equations, the paper hereby compares, mainly graphically, the computational dispersion with analytical solutions for four kinds of 3-dimensional meshes commonly found in mesoscale models, in terms of frequency, horizontal and vertical group velocities. The result indicates that the 3-D mesh C/CP has the best computational dispersion, followed by Z/LZ and Z/LY, with the C/L having the worst performance. It is then known that the C/CP mesh is the most desirable allocation in the design of nonhydrostatic baroclinic models. The mesh has, however, larger errors when dealing with shorter horizontal wavelengths. For the simulation of smaller horizontal scales, the horizontal grid intervals have to be shortened to reduce the errors. Additionally, in view of the dominant use of C/CP mesh in finite-difference models, it should be used in conjunction with the Z/LZ or Z/LY mesh if variables are allocated in spectral models.展开更多
The Global-Regional Integrated forecast System(GRIST)is the next-generation weather and climate integrated model dynamic framework developed by Chinese Academy of Meteorological Sciences.In this paper,we present sever...The Global-Regional Integrated forecast System(GRIST)is the next-generation weather and climate integrated model dynamic framework developed by Chinese Academy of Meteorological Sciences.In this paper,we present several changes made to the global nonhydrostatic dynamical(GND)core,which is part of the ongoing prototype of GRIST.The changes leveraging MPI and PnetCDF techniques were targeted at the parallelization and performance optimization to the original serial GND core.Meanwhile,some sophisticated data structures and interfaces were designed to adjust flexibly the size of boundary and halo domains according to the variable accuracy in parallel context.In addition,the I/O performance of PnetCDF decreases as the number of MPI processes increases in our experimental environment.Especially when the number exceeds 6000,it caused system-wide outages(SWO).Thus,a grouping solution was proposed to overcome that issue.Several experiments were carried out on the supercomputing platform based on Intel x86 CPUs in the National Supercomputing Center in Wuxi.The results demonstrated that the parallel GND core based on grouping solution achieves good strong scalability and improves the performance significantly,as well as avoiding the SWOs.展开更多
A linear diagnostic equation for the nonhydrostatic vertical motion W in severe storms is derived in the Cartesian-earth-spherical coordinates. This W diagnostic equation reveals explicitly how forcing factors work to...A linear diagnostic equation for the nonhydrostatic vertical motion W in severe storms is derived in the Cartesian-earth-spherical coordinates. This W diagnostic equation reveals explicitly how forcing factors work together to exert influence on the nonhydrostatic vertical motion in severe storms. If high-resolution global data are available in Cartesian coordinates with guaranteed quality, the Lax-Crank-Nicolson scheme and the Thomas algorithm might provide a promising numerical solution of this diagnostic equation. As a result, quantitative analyses are expected for the evolution mechanisms of severe storms.展开更多
Intergranular fluids within the nonhydrostatically stressed solids are a sort of important fluids in the crust. Research on the mechanical and chemical behavior of the intergranular fluids in nonhydrostatically stress...Intergranular fluids within the nonhydrostatically stressed solids are a sort of important fluids in the crust. Research on the mechanical and chemical behavior of the intergranular fluids in nonhydrostatically stressed rocks at low temperature is a key for understanding deformation and syntectonic geochemical processes in mid to shallow crust. Theoretically, it is suggested that the fluid film sandwiched between solid grains is one of the main states of intergranular fluids in the nonhydrostatically stressed solids. Their superthin thickness makes the fluid films have the mechanical and chemical behavior very different from the common fluids. Because of hydration force, double layer repulsive force or osmotic pressure due to double layer, the fluid films can transmit nonhydrostatic stress. The solid minerals intergranular fluids interaction and mass transfer by intergranular fluids is stress related, because the stress in solid minerals can enhance the free energy of solid matter on the interfaces. The thermodynamic and kinetic equations for the simple case of stress induced processes are derived.展开更多
This paper examines the simplification strategy of retaining only the nonhydrostatic effect of local acceleration in a three-dimensional fully nonhydrostatic model regarding the submesoscale wave phenomenon in the oce...This paper examines the simplification strategy of retaining only the nonhydrostatic effect of local acceleration in a three-dimensional fully nonhydrostatic model regarding the submesoscale wave phenomenon in the ocean.Elaborate scale analysis of the vertical component of the Reynold-averaged Navier-Stokes(RANS)equation was performed,confirming the rationalization of this simplification.Then,the simplification was implemented in a RANS equation-based nonhydrostatic model NHWAVE(nonhydrostatic WAVE)to make a simplified nonhydrostatic model.Numerical examples were taken to test its performance,including surface sinusoidal waves propagating on an idealized East China Sea topography,tidally induced internal lee waves and small-scale solitary waves.The results show that in a considerably wide range of nonlinear strengths,the simplified nonhydrostatic model can obtain similar results as those in the fully nonhydrostatic model,even for smaller-scale solitary waves.Nonlinearity influences the applicability of the simplification.The stronger the nonlinearity is,the worse the simplified model describes the nonhydrostatic phenomenon.In general,the simplified nonhydrostatic model can simulate surface waves better than internal waves.Improvement of computational efficiency in the simplified nonhydrostatic model is reasonable,reducing the central processing unit time duration in the fully nonhydrostatic model by 16.4%–20.6%.The specially designed algorithm based on the simplified nonhydrostatic equation can remarkably reduce the computational time.展开更多
All solutions of the Korteweg-de Vries(K-dV) equation that are bounded on the real line are physically relevant, depending on the application area of interest. Usually, both analytical and numerical approaches conside...All solutions of the Korteweg-de Vries(K-dV) equation that are bounded on the real line are physically relevant, depending on the application area of interest. Usually, both analytical and numerical approaches consider solution profiles that are either spatially localized or (quasi) periodic. The development of numerical techniques for obtaining approximate solution of partial differential equations has very much increased in the finite element and finite difference methods. Recently, new auxiliary equation method introduced by PANG, BIAN and CHAO is applied to the analytical solution of K-dV equation and wavelet methods are applied to the numerical solution of partial differential equations. Pioneer works in this direction are those of Beylkin, Dahmen, Jaffard and Glowinski, among others. In this research we employ the new auxiliary equation method to obtain the effect of dispersion term on travelling wave solution of K-dV and their numerical estimation as well. Our approach views the limit behavior as an invariant measure of the fast motion drifted by the slow component, where the known constants of motion of the fast system are employed as slowly evolv- ing observables;averaging equations for the latter lead to computation of the characteristic features of the motion.展开更多
The Global/Regional Assimilation and PrEdiction System(GRAPES) is a newly developed global non-hydrostatic numerical prediction model,which will become the next generation medium-range opera-tional model at China Mete...The Global/Regional Assimilation and PrEdiction System(GRAPES) is a newly developed global non-hydrostatic numerical prediction model,which will become the next generation medium-range opera-tional model at China Meteorological Administration(CMA).The dynamic framework of GRAPES is featuring with fully compressible equations,nonhydrostatic or hydrostatic optionally,two-level time semi-Lagrangian and semi-implicit time integration,Charney-Phillips vertical staggering,and complex three-dimensional pre-conditioned Helmholtz solver,etc.Concerning the singularity of horizontal momentum equations at the poles,the polar discretization schemes are described,which include adoption of Arakawa C horizontal grid with ν at poles,incorporation of polar filtering to maintain the computational stability,the correction to Helmholtz equation near the poles,as well as the treatment of semi-Lagrangian interpolation to improve the departure point accuracy,etc.The balanced flow tests validate the rationality of the treatment of semi-Lagrangian departure point calculation and the polar discretization during long time integration.Held and Suarez tests show that the conservation proper-ties of GRAPES model are quite good.展开更多
A modular numerical model was developed for simulating density-stratified flow in domains with irregular bottom topography. The model was designed for examining interactions between stratified flow and topography, e.g...A modular numerical model was developed for simulating density-stratified flow in domains with irregular bottom topography. The model was designed for examining interactions between stratified flow and topography, e.g,, tidally driven flow over two-dimensional sills or internal solitary waves propagating over a shoaling bed. The model was based on the non-hydrostatic vorticity-stream function equations for a continuously stratified fluid in a rotating frame. A self-adaptive grid was adopted in the vertical coordinate, the Alternative Direction Implicit （ADI） scheme was used for the time marching equations while the Poisson equation for stream-function was solved based on the Successive Over Relaxation （SOR） iteration with the Chebyshev acceleration. The numerical techniques were described and three applications of the model were presented.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.42305169)the Basic Research Fund of CAMS(Grant No.2023Y001)the National Key Scientific and Technological Infrastructure project“Earth System Numerical Simulation Facility”(Earth Lab)。
文摘Accurately simulating mesoscale convective systems(MCSs)is essential for predicting global precipitation patterns and extreme weather events.Despite the ability of advanced models to reproduce MCS climate statistics,capturing extreme storm cases over complex terrain remains challenging.This study utilizes the Global–Regional Integrated Forecast System(GRIST)with variable resolution to simulate an eastward-propagating MCS event.The impact of three microphysics schemes,including two single-moment schemes(WSM6,Lin)and one double-moment scheme(Morrison),on the model sensitivity of MCS precipitation simulations is investigated.The results demonstrate that while all the schemes capture the spatial distribution and temporal variation of MCS precipitation,the Morrison scheme alleviates overestimated precipitation compared to the Lin and WSM6 schemes.The ascending motion gradually becomes weaker in the Morrison scheme during the MCS movement process.Compared to the runs with convection parameterization,the explicit-convection setup at 3.5-km resolution reduces disparities in atmospheric dynamics due to microphysics sensitivity in terms of vertical motions and horizontal kinetic energy at the high-wavenumber regimes.The explicit-convection setup more accurately captures the propagation of both main and secondary precipitation centers during the MCS development,diminishing the differences in both precipitation intensity and propagation features between the Morrison and two single-moment schemes.These findings underscore the importance of microphysics schemes for global nonhydrostatic modeling at the kilometer scale.The role of explicit convection for reducing model uncertainty is also outlined.
基金supported by the National Science Foundation of China(Grant No.42230606)。
文摘Here,a nonhydrostatic alternative scheme(NAS)is proposed for the grey zone where the nonhydrostatic impact on the atmosphere is evident but not large enough to justify the necessity to include an implicit nonhydrostatic solver in an atmospheric dynamical core.The NAS is designed to replace this solver,which can be incorporated into any hydrostatic models so that existing well-developed hydrostatic models can effectively serve for a longer time.Recent advances in machine learning(ML)provide a potential tool for capturing the main complicated nonlinear-nonhydrostatic relationship.In this study,an ML approach called a neural network(NN)was adopted to select leading input features and develop the NAS.The NNs were trained and evaluated with 12-day simulation results of dry baroclinic-wave tests by the Weather Research and Forecasting(WRF)model.The forward time difference of the nonhydrostatic tendency was used as the target variable,and the five selected features were the nonhydrostatic tendency at the last time step,and four hydrostatic variables at the current step including geopotential height,pressure in two different forms,and potential temperature,respectively.Finally,a practical NAS was developed with these features and trained layer by layer at a 20-km horizontal resolution,which can accurately reproduce the temporal variation and vertical distribution of the nonhydrostatic tendency.Corrected by the NN-based NAS,the improved hydrostatic solver at different horizontal resolutions can run stably for at least one month and effectively reduce most of the nonhydrostatic errors in terms of system bias,anomaly root-mean-square error,and the error of the wave spatial pattern,which proves the feasibility and superiority of this scheme.
基金supported by the National Natural Science Foundation of China under Grant No.11504354Research Foundation of National Key Laboratory of Shock Wave and Detonation Physics under Grants No.9140C6703010703 and 9140C6703010803.
文摘The equations of state(EOSs)of materials are the cornerstone of condensed matter physics,material science,and geophysics.However,acquiring an accurate EOS in diamond anvil cell(DAC)experiments continues to prove problematic because the current lack of an accurate pressure scale with clarified sources of uncertainty makes it difficult to determine a precise pressure value at high pressure,and nonhydrostaticity affects both the volume and pressure determination.This study will discuss the advantages and drawbacks of various pressure scales,and propose an absolute pressure scale and correction methods for the effects of non-hydrostaticity.At the end of this paper,we analyze the accuracy of the determined EOS in the DAC experiments we can achieve to date.
基金supported by the National Natural Science Foundation of China (Grant No. 41175095)the National Key Technology R&D Program(Grant No. 2012BAC22B01)a research project of the Chinese Academy of Meteorological Sciences (Grant No. 2014Z001)
文摘A 3D dynamic core of the non-hydrostatic model GRAPES（Global/Regional Assimilation and Prediction System） is developed on the Yin-Yang grid to address the polar problem and to enhance the computational efficiency. Three-dimensional Coriolis forcing is introduced to the new core, and full representation of the Coriolis forcing makes it straightforward to share code between the Yin and Yang subdomains. Similar to that in the original GRAPES model, a semi-implicit semi-Lagrangian scheme is adopted for temporal integration and advection with additional arrangement for cross-boundary transport. Under a non-centered second-order temporal and spatial discretization, the dry nonhydrostatic frame is summarized as the solution of an elliptical problem. The resulting Helmholtz equation is solved with the Generalized Conjugate Residual solver in cooperation with the classic Schwarz method. Even though the coefficients of the equation are quite different from those in the original model, the computational procedure of the new core is just the same. The bi-cubic Lagrangian interpolation serves to provide Dirichlet-type boundary conditions with data transfer between the subdomains. The dry core is evaluated with several benchmark test cases, and all the tests display reasonable numerical stability and computing performance. Persistency of the balanced flow and development of both the mountain-induced Rossby wave and Rossby–Haurwitz wave confirms the appropriate installation of the 3D Coriolis terms in the semi-implicit semi-Lagrangian dynamic core on the Yin-Yang grid.
基金supported by the National Key Research and Development Program of China (Grant Nos. 2017YFC1501901 and 2017YFA0603901)the Beijing Natural Science Foundation (Grant No. JQ18001)
文摘A 3D compressible nonhydrostatic dynamic core based on a three-point multi-moment constrained finite-volume (MCV) method is developed by extending the previous 2D nonhydrostatic atmospheric dynamics to 3D on a terrainfollowing grid. The MCV algorithm defines two types of moments: the point-wise value (PV) and the volume-integrated average (VIA). The unknowns (PV values) are defined at the solution points within each cell and are updated through the time evolution formulations derived from the governing equations. Rigorous numerical conservation is ensured by a constraint on the VIA moment through the flux form formulation. The 3D atmospheric dynamic core reported in this paper is based on a three-point MCV method and has some advantages in comparison with other existing methods, such as uniform third-order accuracy, a compact stencil, and algorithmic simplicity. To check the performance of the 3D nonhydrostatic dynamic core, various benchmark test cases are performed. All the numerical results show that the present dynamic core is very competitive when compared to other existing advanced models, and thus lays the foundation for further developing global atmospheric models in the near future.
基金The National Natural Science Foundation of China under contract Nos 41528601 and 41376029the Youth Innovation Promotion Association of Chinese Academy of Sciences under contract No.Y4KY07103Lthe Strategic Priority Research Program of the Chinese Academy of Sciences under contract No.XDA11020101
文摘A nonhydrostatic numerical model was developed and numerical experiments performed on the interaction of an internal solitary wave （ISW） with a sill, for a two-layer fluid with a diffusive interface. Based on the blocking parameter （Br）, the flow was classified into three cases： （1） when bottom topography has little influence on the propagation and spatial structure of the ISW （Br〈0.5）, （2） where the ISW is distorted significantly by the blocking effect of the topography （though no wave breaking occurs, （0.5〈Br〈0.7）, and （3） where the ISW is broken as it encounters and passes over the bottom topography （0.7〈Br）. The numerical results obtained here are consistent with those obtained in laboratory experiments. The breaking process of the incident ISW when Br=0.7 was completely reproduced. Dissipation rate was linearly related to the blocking parameter when B,〈0.7, and the maximum dissipation rate could reach about 34% as Br raised to about 1.0. After that, instead of breaking, more reflection happened. Similarly, breaking induced mixing was also most effective during Br around 1.0, and can be up to 0.16.
文摘A high resolution nonhydrostatic tropical atmospheric model is developed by using a ready-made regional atmospheric modeling system. The motivation is to investigate the convective activities associated with the tropical intraseasonal oscillation (ISO) through a cloud resolving calculation. Due to limitations in computing resources, a
基金supported by the China Meteorological Administration Special Fund for numerical prediction(GRAPES)the National Natural Science Foundation of China(Grant Nos.40775067)
文摘With the development of numerical weather prediction technology, the traditional global hydrostatic models used in many countries of the world for operational weather forecasting and numerical simulations of general circulation have become more and more unfit for high-impact weather prediction. To address this, it is important to invest in the development of global nonhydrostatic models. Few existing nonhydrostatic global models use consistently the grid finite difference scheme for the primitive equations of dynamical cores, which can subsequently degrade the accuracy of the calculations. A new nonhydrostatic global spectral model, which utilizes the Eulerian spectral method, is developed here from NCAR Community Atmosphere Model 3.0 （CAM3.0）. Using Janjic＇s hydrostatic/nonhydrostatic method, a global nonhydrostatic spectral method for the primitive equations has been formulated and developed. In order to retain the integrity of the nonhydrostatic equations, the atmospheric curvature correction and eccentricity correction are considered. In this paper, the Held-Suarez idealized test and an idealized baroclinic wave test are first carried out, which shows that the nonhydrostatic global spectral model has similar climate states to the results of many other global models for long-term idealized integration, as well as better simulation ability for short-term idealized integration. Then, a real case experiment is conducted using the new dynamical core with the full physical parameterizations of subgrid-scale physical processes. The 10-day numerical integration indicates a decrease in systematic error and a better simulation of zonal wind, temperature, and 500-hPa height.
基金The National Key Research and Development Program of China under contract No.2016YFC1402705the National Natural Science Foundation of China under contract No.41576189
文摘Nonlinear internal waves(NIWs) are ubiquitous around the Kara Sea, a part of the Arctic Ocean that is north of Siberia. Three hot spot sources for internal waves, one of which is the Kara Strait, have been identified based on Envisat ASAR. The generation and evolution of the NIWs through the interactions of the tide and topography across the strait is studied based on a nonhydrostatic numerical model. The model captures most wave characteristics shown by satellite data. A typical inter-packets distance on the Barents Sea side is about 25 km in summer, with a phase speed about 0.65 m/s. A northward background current may intensify the accumulation of energy during generation, but it has little influence on the other properties of the generated waves. The single internal solitary wave(ISW) structure is a special phenomenon that follows major wave trains, with a distance about 5–8 km. This wave is generated with the leading wave packets during the same tidal period. When a steady current toward the Kara Sea is included, the basic generation process is similar, but the waves toward the Kara Sea weaken and display an internal bore-like structure with smaller amplitude than in the control experiment. In winter, due to the growth of sea ice, stratification across the Kara Strait is mainly determined by the salinity, with an almost uniform temperature close to freezing. A pycnocline deepens near the middle of the water depth(Barents Sea side), and the NIWs process is not as important as the NIWs process in summer. There is no fission process during the simulation.
文摘A high resolution, nonhydrostatic, three dimensional diagnostic PBL model over small scale concave terrain was established in this paper. A two dimensional prognostic model was developed based on the diagnostic model. The hydrostatic approximation was abandoned and the simple energy ( E e ) closure scheme was used in both models. Using the two models, characteristics of PBL structure and its evolution were fully studied. The main characteristic of the PBL is the circulation, and it fairly affects the distribution of the pollutant in the pit.
文摘The potential temperature vorticity has been introduced to polish the (momentum) vorticity - streamfunction method for solving the two-dimensional and nonhydrostatic model with much accuracy but not many increments of computation. The three-step procedure introduced in the present paper can be used to solve both shallow and deep dynamic models.
基金supported by The National Key Research and Development Program of China(Grants Nos.2017YFA0603901 and 2017YFC1501901)The National Natural Science Foundation of China(Grant No.41522504)。
文摘An adaptive 2 D nonhydrostatic dynamical core is proposed by using the multi-moment constrained finite-volume(MCV) scheme and the Berger-Oliger adaptive mesh refinement(AMR) algorithm. The MCV scheme takes several pointwise values within each computational cell as the predicted variables to build high-order schemes based on single-cell reconstruction. Two types of moments, such as the volume-integrated average(VIA) and point value(PV), are defined as constraint conditions to derive the updating formulations of the unknowns, and the constraint condition on VIA guarantees the rigorous conservation of the proposed model. In this study, the MCV scheme is implemented on a height-based, terrainfollowing grid with variable resolution to solve the nonhydrostatic governing equations of atmospheric dynamics. The AMR grid of Berger-Oliger consists of several groups of blocks with different resolutions, where the MCV model developed on a fixed structured mesh can be used directly. Numerical formulations are designed to implement the coarsefine interpolation and the flux correction for properly exchanging the solution information among different blocks. Widely used benchmark tests are carried out to evaluate the proposed model. The numerical experiments on uniform and AMR grids indicate that the adaptive model has promising potential for improving computational efficiency without losing accuracy.
基金Supported by the open research program of LASG Institute of Atmospheric Physics Chinese Academy of Sciences
文摘Forecasts and simulations are varied owing to different allocation of 3-dimensional variables in mesoscale models. No attempts have been made to address the issue of optimizing the simulation with a 3-dimensional variables distribution that should come to be. On the basis of linear nonhydrostatic anelastic equations, the paper hereby compares, mainly graphically, the computational dispersion with analytical solutions for four kinds of 3-dimensional meshes commonly found in mesoscale models, in terms of frequency, horizontal and vertical group velocities. The result indicates that the 3-D mesh C/CP has the best computational dispersion, followed by Z/LZ and Z/LY, with the C/L having the worst performance. It is then known that the C/CP mesh is the most desirable allocation in the design of nonhydrostatic baroclinic models. The mesh has, however, larger errors when dealing with shorter horizontal wavelengths. For the simulation of smaller horizontal scales, the horizontal grid intervals have to be shortened to reduce the errors. Additionally, in view of the dominant use of C/CP mesh in finite-difference models, it should be used in conjunction with the Z/LZ or Z/LY mesh if variables are allocated in spectral models.
基金This work was supported by the National Key Research and Development Program of China under Grant No.2017YFC1502203.
文摘The Global-Regional Integrated forecast System(GRIST)is the next-generation weather and climate integrated model dynamic framework developed by Chinese Academy of Meteorological Sciences.In this paper,we present several changes made to the global nonhydrostatic dynamical(GND)core,which is part of the ongoing prototype of GRIST.The changes leveraging MPI and PnetCDF techniques were targeted at the parallelization and performance optimization to the original serial GND core.Meanwhile,some sophisticated data structures and interfaces were designed to adjust flexibly the size of boundary and halo domains according to the variable accuracy in parallel context.In addition,the I/O performance of PnetCDF decreases as the number of MPI processes increases in our experimental environment.Especially when the number exceeds 6000,it caused system-wide outages(SWO).Thus,a grouping solution was proposed to overcome that issue.Several experiments were carried out on the supercomputing platform based on Intel x86 CPUs in the National Supercomputing Center in Wuxi.The results demonstrated that the parallel GND core based on grouping solution achieves good strong scalability and improves the performance significantly,as well as avoiding the SWOs.
基金supported by the National Natural Science Foundation of China under Grant Nos.40175018 and 40275026.
文摘A linear diagnostic equation for the nonhydrostatic vertical motion W in severe storms is derived in the Cartesian-earth-spherical coordinates. This W diagnostic equation reveals explicitly how forcing factors work together to exert influence on the nonhydrostatic vertical motion in severe storms. If high-resolution global data are available in Cartesian coordinates with guaranteed quality, the Lax-Crank-Nicolson scheme and the Thomas algorithm might provide a promising numerical solution of this diagnostic equation. As a result, quantitative analyses are expected for the evolution mechanisms of severe storms.
文摘Intergranular fluids within the nonhydrostatically stressed solids are a sort of important fluids in the crust. Research on the mechanical and chemical behavior of the intergranular fluids in nonhydrostatically stressed rocks at low temperature is a key for understanding deformation and syntectonic geochemical processes in mid to shallow crust. Theoretically, it is suggested that the fluid film sandwiched between solid grains is one of the main states of intergranular fluids in the nonhydrostatically stressed solids. Their superthin thickness makes the fluid films have the mechanical and chemical behavior very different from the common fluids. Because of hydration force, double layer repulsive force or osmotic pressure due to double layer, the fluid films can transmit nonhydrostatic stress. The solid minerals intergranular fluids interaction and mass transfer by intergranular fluids is stress related, because the stress in solid minerals can enhance the free energy of solid matter on the interfaces. The thermodynamic and kinetic equations for the simple case of stress induced processes are derived.
基金The National Natural Science Foundation of China under contract No.41676003.
文摘This paper examines the simplification strategy of retaining only the nonhydrostatic effect of local acceleration in a three-dimensional fully nonhydrostatic model regarding the submesoscale wave phenomenon in the ocean.Elaborate scale analysis of the vertical component of the Reynold-averaged Navier-Stokes(RANS)equation was performed,confirming the rationalization of this simplification.Then,the simplification was implemented in a RANS equation-based nonhydrostatic model NHWAVE(nonhydrostatic WAVE)to make a simplified nonhydrostatic model.Numerical examples were taken to test its performance,including surface sinusoidal waves propagating on an idealized East China Sea topography,tidally induced internal lee waves and small-scale solitary waves.The results show that in a considerably wide range of nonlinear strengths,the simplified nonhydrostatic model can obtain similar results as those in the fully nonhydrostatic model,even for smaller-scale solitary waves.Nonlinearity influences the applicability of the simplification.The stronger the nonlinearity is,the worse the simplified model describes the nonhydrostatic phenomenon.In general,the simplified nonhydrostatic model can simulate surface waves better than internal waves.Improvement of computational efficiency in the simplified nonhydrostatic model is reasonable,reducing the central processing unit time duration in the fully nonhydrostatic model by 16.4%–20.6%.The specially designed algorithm based on the simplified nonhydrostatic equation can remarkably reduce the computational time.
文摘All solutions of the Korteweg-de Vries(K-dV) equation that are bounded on the real line are physically relevant, depending on the application area of interest. Usually, both analytical and numerical approaches consider solution profiles that are either spatially localized or (quasi) periodic. The development of numerical techniques for obtaining approximate solution of partial differential equations has very much increased in the finite element and finite difference methods. Recently, new auxiliary equation method introduced by PANG, BIAN and CHAO is applied to the analytical solution of K-dV equation and wavelet methods are applied to the numerical solution of partial differential equations. Pioneer works in this direction are those of Beylkin, Dahmen, Jaffard and Glowinski, among others. In this research we employ the new auxiliary equation method to obtain the effect of dispersion term on travelling wave solution of K-dV and their numerical estimation as well. Our approach views the limit behavior as an invariant measure of the fast motion drifted by the slow component, where the known constants of motion of the fast system are employed as slowly evolv- ing observables;averaging equations for the latter lead to computation of the characteristic features of the motion.
基金Supported by the Ministry of Science and Technology of China (Grant Nos 2006BAC02B01 and 2006BAC03B03)the National High Technology Research and Development Program of China (863 Program) (Grant No 2006AA01A123)
文摘The Global/Regional Assimilation and PrEdiction System(GRAPES) is a newly developed global non-hydrostatic numerical prediction model,which will become the next generation medium-range opera-tional model at China Meteorological Administration(CMA).The dynamic framework of GRAPES is featuring with fully compressible equations,nonhydrostatic or hydrostatic optionally,two-level time semi-Lagrangian and semi-implicit time integration,Charney-Phillips vertical staggering,and complex three-dimensional pre-conditioned Helmholtz solver,etc.Concerning the singularity of horizontal momentum equations at the poles,the polar discretization schemes are described,which include adoption of Arakawa C horizontal grid with ν at poles,incorporation of polar filtering to maintain the computational stability,the correction to Helmholtz equation near the poles,as well as the treatment of semi-Lagrangian interpolation to improve the departure point accuracy,etc.The balanced flow tests validate the rationality of the treatment of semi-Lagrangian departure point calculation and the polar discretization during long time integration.Held and Suarez tests show that the conservation proper-ties of GRAPES model are quite good.
基金Project supported by the National Science and Technology Supporting Plan (Grant No. 2006BAB18B03).
文摘A modular numerical model was developed for simulating density-stratified flow in domains with irregular bottom topography. The model was designed for examining interactions between stratified flow and topography, e.g,, tidally driven flow over two-dimensional sills or internal solitary waves propagating over a shoaling bed. The model was based on the non-hydrostatic vorticity-stream function equations for a continuously stratified fluid in a rotating frame. A self-adaptive grid was adopted in the vertical coordinate, the Alternative Direction Implicit （ADI） scheme was used for the time marching equations while the Poisson equation for stream-function was solved based on the Successive Over Relaxation （SOR） iteration with the Chebyshev acceleration. The numerical techniques were described and three applications of the model were presented.
