A Neural-network-based Alternative Scheme to Include Nonhydrostatic Processes in an Atmospheric Dynamical Core

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.

Analysis of a simplification strategy in a nonhydrostatic model for surface and internal wave problems

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.

A High Resolution Nonhydrostatic Tropical Atmospheric Model and Its Performance

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

The Development of a Nonhydrostatic Global Spectral Model

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.

A 3D Nonhydrostatic Compressible Atmospheric Dynamic Core by Multi-moment Constrained Finite Volume Method

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.

An Adaptive Nonhydrostatic Atmospheric Dynamical Core Using a Multi-Moment Constrained Finite Volume Method

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.

Improving the Vorticity-Streamfunction Method to Solve Two-Dimensional Anelastic and Nonhydrostatic Model

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.

A Linear Diagnostic Equation for the Nonhydrostatic Vertical Motion W in Severe Storms

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.

Parallelization and I/O Performance Optimization of a Global Nonhydrostatic Dynamical Core Using MPI

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.

Mechanical and chemical behavior of intergranular fluids in nonhydrostatically stressed rocks at low temperature

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.

Climatic impacts induced by winter wheat irrigation over North China simulated by the nonhydrostatic RegCM4.7

Quantification of the impact of winter wheat irrigation on the climate and the occurrence of extreme climatic events over North China is crucial for regional adaptation planning.Previous related studies mainly focused on the impact on surface processes;however,few focused on the effects of extreme events using high-resolution nonhydrostatic regional climate models.Here,the 9-km-resolution nonhydrostatic RegCM4.7 was coupled with a crop irrigation scheme and an updated winter wheat irrigation dataset to better simulate irrigation effects.Two experiments were conducted with and without winter wheat irrigation to isolate the effects of irrigation.Results showed that irrigation simulation reduces the model biases in temperature,precipitation,latent heat flux,soil moisture,sensitive heat flux,and top-layer soil moisture.Moreover,it also reduces the bias and increases the correlation with observations obtained in irrigated areas,especially in summer,indicating better representation of irrigation schemes.Winter wheat irrigation tends to cause substantial cooling of the local surface maximum,minimum,and mean air temperatures(by-1.68,-0.34,and-0.79℃,respectively)over irrigated areas of North China,with the largest changes observed in relation to maximum temperature.Additionally,precipitation is found to increase during spring and summer,which is strongly related to water vapor transport in the lower levels of the atmosphere.Further analyses indicated that the number of annual mean hot days decrease(-13.9 d),whereas the number of both comfort days(+10.2 d)and rainy days(days with total precipitation greater than 1 mm:+6.6 d)increase over irrigated areas,demonstrating beneficial feedback to human perception and agriculture.Fortunately,although the heat wave risk increases(number of annual mean heat wave days:+5.8 d),the impact is limited to small areas within irrigated region.Additionally,no notable change was found in terms of heavy rainfall events and precipitation intensity,which might be an undereastimation caused by the less water use in model simulation.Although winter wheat irrigation does not have notable impact on the climate of the surrounding region,it is an important factor for the local-scale climate.

Verification of a Modified Nonhydrostatic Global Spectral Dynamical Core Based on the Dry-Mass Vertical Coordinate: Three-Dimensional Idealized Test Cases

The newly developed nonhydrostatic(NH)global spectral dynamical core is evaluated by using three-dimensional(3D)benchmark tests with/without moisture.This new dynamical core differs from the original Aladin-NH like one in the combined use of a dry-mass vertical coordinate and a new temperature variable,and thus,it inherently conserves the dry air mass and includes the mass sink effect associated with precipitation flux.Some 3D dry benchmark tests are first conducted,including steady state,dry baroclinic waves,mountain waves in non-sheared and sheared background flows,and a dry Held–Suarez test.The results from these test cases demonstrate that the present dynamical core is accurate and robust in applications on the sphere,especially for addressing the nonhydrostatic effects.Then,three additional moist test cases are conducted to further explore the improvement of the new dynamical core.Importantly,in contrast to the original Aladin-NH like one,the new dynamical core prefers to obtain simulated tropical cyclone with lower pressure,stronger wind speeds,and faster northward movement,which is much closer to the results from the Model for Prediction Across Scales(MPAS),and it also enhances the updrafts and provides enhanced precipitation rate in the tropics,which partially compensates the inefficient vertical transport due to the absence of the deep convection parameterization in the moist Held–Suarez test,thus demonstrating its potential value for full-physics global NH numerical weather prediction application.

A semi-implicit semi-Lagrangian global nonhydrostatic model and the polar discretization scheme

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.

A NONHYDROSTATIC NUMERICAL MODEL FOR DENSITY STRATIFIED FLOW AND ITS APPLICATIONS

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.

Developments of the Three-Dimensional Variational Data Assimilation System for the Nonhydrostatic GRAPES

Based on the original GRAPES（Global/Regional Assimilation and PrEdiction System）3DVAR（p3DAR）, which is defined on isobaric surface,a new three-dimensional variational data assimilation system（m3DVAR） is constructed and used exclusively with the nonhydrostatic GRAPES model in order to reduce the errors caused by spatial interpolation and variable transformation,and to improve the quality of the initial value for operational weather forecasts.Analytical variables of the m3DVAR are fully consistent with predictands of the GRADES model in terms of spatial staggering and physical definition.A different vertical coordinate and the nonhydrostatic condition are taken into account,and a new scheme for solving the dynamical constraint equations is designed for the m3DVAR.To deal with the diffculties in solving the nonlinear balance equation atσlevels,dynamical balance constraints between mass and wind fields are reformulated,and an effective mathematical scheme is implemented under the terrain-following coordinate.Meanwhile,new observation operators are developed for routine observational data,and the background error covariance is also obtained.Currently,the m3DVAR system can assimilate all routine observational data. Multi-variable idealized experiments with single point observations are performed to validate the m3DVAR system.The results show that the system can describe correctly the multi-variable analysis and the relationship of the physical constraints.The difference of innovation and the analysis residual forπalso show that the analysis error of the m3DVAR is smaller than that of the p3DVAR.The T s scores of precipitation forecasts in August 2006 indicate that the m3DVAR system provides reduced errors in the model initial value than the p3DVAR system.Therefore,the m3DVAR system can improve the analysis quality and initial value for numerical weather predictions.

GPU acceleration of a nonhydrostatic model for the internal solitary waves simulation

The parallel computing algorithm for a nonhydrostatic model on one or multiple Graphic Processing Units （GPUs） for the simulation of internal solitary waves is presented and discussed. The computational efficiency of the GPU scheme is analyzed by a series of numerical experiments, including an ideal case and the field scale simulations, performed on the workstation and the super- computer system. The calculated results show that the speedup of the developed GPU-based parallel computing scheme, compared to the implementation on a single CPU core, increases with the number of computational grid cells, and the speedup can increase quasi- linearly with respect to the number of involved GPUs for the problem with relatively large number of grid cells within 32 GPUs.

NONHYDROSTATIC NUMERICAL SIMULATION FOR THE“96.8”EXTRAORDINARY RAINSTORM AND THE DEVELOPING STRUCTURE OF MESOSCALE SYSTEM

During the period of 3—5 August 1996(for short “96.8”),an extraordinary rainstorm event occurred in Henan,Hebei and Shanxi Provinces in China,resulting in severe flood catastrophe. Synoptic analyses indicated that the stable gross col field and the interaction between a northward moving typhoon(down into low pressure)and its east lateral Pacific subtropical high were the large-and meso-scale circulation conditions of the “96.8” extraordinary rainstorm.The mesoscale typhoon-low and its specific dynamical and thermodynamical structures were directly related to this rainstorm event.The nonhydrostatic version of mesoscale numerical model MM5 was used to conduct investigation of numerical simulation for this case.The simulation with the full physical processes of nonhydrostatic version MM5 was basically possessed of a capability to reproduce the genesis,development and evolution of the large-scale and meso-α scale synoptic systems.The simulative results using a two-way interactive nesting procedure revealed that the typhoon-low was possessed of an intensive coupled mechanism between the dynamical and thermodynamical fields, namely,the developing typhoon-low was possessed of a structure of the.cyclonic vorticity column with warm center and high humidity,the vorticity column on the lower levels was the moist convective instability and negative moist potential vorticity structure:the intensive ascending vertical motion and the intense divergence on upper levels and intensive convergence on the lower levels as well as the development of the convective cloud cluster were intercoupling:the intense southern wind jet companied by the typhoon-low was not only the interaccompanying and intercoupling condition of the development and maintenance of the typhoon-low and convective cloud cluster,but also was the transportable belt of the moisture source and heat energy of the “96.8”extraordinary rainstorm.The analysis of simulative results of precipitation indicated that the distribution of the rainfall belt and rainfall rate was basically consistent with that of the observation in spite of some rainfall centers less or larger than those of the observation for coarse or fine mesh domain,respectively.

Modeling the interaction of an internal solitary wave with a sill

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.

An Improved Dynamic Core for a Non-hydrostatic Model System on the Yin-Yang Grid

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.

A numerical simulation of the generation and evolution of nonlinear internal waves across the Kara Strait

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.