Improved Diurnal Cycle of Precipitation on Land in a Global Non-Hydrostatic Model Using a Revised NSAS Deep Convective Scheme

In relatively coarse-resolution atmospheric models,cumulus parameterization helps account for the effect of subgridscale convection,which produces supplemental rainfall to the grid-scale precipitation and impacts the diurnal cycle of precipitation.In this study,the diurnal cycle of precipitation was studied using the new simplified Arakawa-Schubert scheme in a global non-hydrostatic atmospheric model,i.e.,the Yin-Yang-grid Unified Model for the Atmosphere.Two new diagnostic closures and a convective trigger function were suggested to emphasize the job of the cloud work function corresponding to the free tropospheric large-scale forcing.Numerical results of the 0.25-degree model in 3-month batched real-case simulations revealed an improvement in the diurnal precipitation variation by using a revised trigger function with an enhanced dynamical constraint on the convective initiation and a suitable threshold of the trigger.By reducing the occurrence of convection during peak solar radiation hours,the revised scheme was shown to be effective in delaying the appearance of early-afternoon rainfall peaks over most land areas and accentuating the nocturnal peaks that were wrongly concealed by the more substantial afternoon peak.In addition,the revised scheme enhanced the simulation capability of the precipitation probability density function,such as increasing the extremely low-and high-intensity precipitation events and decreasing small and moderate rainfall events,which contributed to the reduction of precipitation bias over mid-latitude and tropical land areas.

Analysis and Evaluation of the Global Aerosol Optical Properties Simulated by an Online Aerosol-coupled Non-hydrostatic Icosahedral Atmospheric Model

Aerosol optical properties are simulated using the Spectral Radiation Transport Model I~）r Aerosol Species （SPRINTARS） coupled with the Non-hydrostatic ICosahedral Atmospheric Model （NICAM）. The 3-year global mean all-sky aerosol optical thickness （AOT） at 550 nm, theAngstr/Sm Exponent （AE） based on AOTs at 440 and 870 nm, and the single scattering albedo （SSA） at 550 nm are estimated at 0.123, 0.657 and 0.944, respectively. For each aerosol species, the mean AOT is within the range of the AeroCom models. Both the modeled all-sky and clear-sky results are compared with observations from the Moderate Resolution Imaging Spectroradiometer （MODIS） and the Aerosol Robotic Network （AERONET）. The simulated spatiotemporal distributions of all-sky AOTs can generally reproduce the MODIS retrievals, and the correlation and model skill can be slightly improved using the clear-sky results over most land regions. The differences between clear-sky and all-sky AOTs are larger over polluted regions. Compared with observations from AERONET, the modeled and observed all-sky AOTs and AEs are generally in reasonable agreement, whereas the SSA variation is not well captured. Although the spatiotemporal distributions of all-sky and clear-sky results are similar, the clear-sky results are generally better correlated with the observations. The clear-sky AOT and SSA are generally lower than the all-sky results, especially in those regions where the aerosol chemical composition is contributed to mostly by sulfate aerosol. The modeled clear-sky AE is larger than the all-sky AE over those regions dominated by hydrophilic aerosol, while the＇opposite is found over regions dominated by hydrophobic aerosol.

A Hybrid Finite-Volume and Finite Difference Scheme for Depth- Integrated Non-Hydrostatic Model

A depth-integrated, non-hydrostatic model with hybrid finite difference and finite volume numerical algorithm is proposed in this paper. By utilizing a fraction step method, the governing equations are decomposed into hydrostatic and non-hydrostatic parts. The first part is solved by using the finite volume conservative discretization method, whilst the latter is considered by solving discretized Poisson-type equations with the finite difference method. The second-order accuracy, both in time and space, of the finite volume scheme is achieved by using an explicit predictor-correction step and linear construction of variable state in cells. The fluxes across the cell faces are computed in a Godunov-based manner by using MUSTA scheme. Slope and flux limiting technique is used to equip the algorithm with total variation dimensioning property for shock capturing purpose. Wave breaking is treated as a shock by switching off the non-hydrostatic pressure in the steep wave front locally. The model deals with moving wet/dry front in a simple way. Numerical experiments are conducted to verify the proposed model.

A Higher-Efficient Non-Hydrostatic Finite Volume Model for Strong Three-Dimensional Free Surface Flows and Sediment Transport

In order to accurately simulate strong three-dimensional （3-D） free surface flows and sediment transport, the fully 3- D non-hydrostatic pressure models are developed based on the incompressible Navier-Stokes equations and convection-diffusion equation of sediment concentration with the mixing triangle and quadrilateral grids. The governing equations are discretized with the unstructured finite volume method in order to provide conservation properties of mass and momentum, and flexibility with practical application. It is shown that it is first-order accurate on nonuniform plane two-dimensional （2-D） grids and second-order accurate on uniform plane grids. A third-order approximation of the vertical velocity at the top-layer is applied. In such a way, free surface zero stress boundary condition is satisfied maturely, and very few vertical layers are needed to give an accurate solution even for complex discontinuous flow and short wave simulation. The model is applied to four examples to simulate strong 3-D free surface flows and sediment transport where non-hydrostatic pressures have a considerable effect on the velocity field. The newly developed model is verified against analytical solutions with an excellent agreement.

Two-Layer Non-Hydrostatic Model for Generation and Propagation of Interfacial Waves

When pycnocline thickness of ocean density is relatively small, density stratification can be well represented as a two-layer system. In this article, a depth integrated model of the two-layer fluid with constant density is considered,and a variant of the edge-based non-hydrostatic numerical scheme is formulated. The resulting scheme is very efficient since it resolves the vertical fluid depth only in two layers. Despite using just two layers, the numerical dispersion is shown to agree with the analytical dispersion curves over a wide range of kd, where k is the wave number and d the water depth. The scheme was tested by simulating an interfacial solitary wave propagating over a flat bottom, as well as over a bottom step. On a laboratory scale, the formation of an interfacial wave is simulated,which also shows the interaction of wave with a triangular bathymetry. Then, a case study using the Lombok Strait topography is discussed, and the results show the development of an interfacial wave due to a strong current passing through a sill.

Non-hydrostatic modelling of regular wave transformation and current circulation in an idealized reef-lagoon-channel system

The wave-induced setup and circulation in a two dimensional horizontal(2DH)reef-lagoon-channel system is investigated by a non-hydrostatic model.The simulated results agree well with observations from the laboratory experiments,revealing that the model is valid in simulating wave transformation and currents over reefs.The effects of incident wave height,period,and reef flat water depth on the mean sea level and wave-driven currents are examined.Results show that the distributions of mean sea level and current velocities on the reef flat adjacent to the channel vary significantly from those in the area close to the side walls.From the wave averaged current field,an obvious alongshore flux flowing from the reef flat to the channel is captured.The flux from the reef flat composes the second source of the offshore rip current,while the first source is from the lagoon.A detailed momentum balance analysis shows that the alongshore current is mainly induced by the pressure gradient between the reef flat and the channel.In the lagoon,the momentum balances are between the pressure and radiation stress gradient,which drives flow towards the channel.Along the channel,the offshore current is mainly driven by the pressure gradient.

Vertical two-dimensional non-hydrostatic pressure model with single layer

The vertical two-dimensional non-hydrostatic pressure models with multiple layers can make prediction more accurate than those obtained by the hydrostatic pres- sure assumption. However, they are time-consuming and unstable, which makes them unsuitable for wider application. In this study, an efficient model with a single layer is developed. Decomposing the pressure into the hydrostatic and dynamic components and integrating the x-momentum equation from the bottom to the free surface can yield a horizontal momentum equation, in which the terms relevant to the dynamic pressure are discretized semi-implicitly. The convective terms in the vertical momentum equation are ignored, and the rest of the equation is approximated with the Keller-box scheme. The velocities expressed as the unknown dynamic pressure are substituted into the continuity equation, resulting in a tri-diagonal linear system solved by the Thomas algorithm. The validation of solitary and sinusoidal waves indicates that the present model can provide comparable results to the models with multiple layers but at much lower computation cost.

Exact solutions of (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations

The symmetries and the exact solutions of the （3＋l）-dimensional nonlinear incompressible non-hydrostatic Boussi- nesq （INHB） equations, which describe atmospheric gravity waves, are studied in this paper. The calculation on symmetry shows that the equations are invariant under the Galilean transformations, the scaling transformations, and the space-time translations. Three types of symmetry reduction equations and similar solutions for the （3＋ 1）-dimensional INHB equations are proposed. Traveling and non-traveling wave solutions of the INHB equations are demonstrated. The evolutions of the wind velocities in latitudinal, longitudinal, and vertical directions with space-time are demonstrated. The periodicity and the atmosphere viscosity are displayed in the （3＋1）-dimensional INHB system.

High-resolution tsunami hazard assessment for the Guangdong-Hong Kong-Macao Greater Bay Area based on a non-hydrostatic tsunami model

The Guangdong-Hong Kong-Macao Greater Bay Area(GBA)is threatened by potential tsunami hazards from the Littoral Fault Zone(LFZ)and the Manila subduction zone(MSZ),and may suffer huge damage because of its dense population,concentrated infrastructure,and low-lying coasts.Previous tsunami studies for the GBA made simple assumptions on the mechanisms of LFZ earthquakes,and used coarse bathymetry data in tsunami simulation,which limited the prediction of detailed tsunami hazard characteristics.In this paper,we develop a parallel dispersive tsunami model PCOMCOT to efficiently simulate dispersive,nonlinear,and breaking tsunami waves.We also construct large-scale and high-resolution bathymetry models for the GBA by correcting and integrating various data sources.Dynamic rupture simulation is performed for the LFZ to obtain a more reliable earthquake source model.We propose several representative earthquake scenarios for the LFZ and MSZ,and use PCOMCOT to calculate the resulting tsunami waves,currents,and inundation in the GBA.Our results indicate that if an M_(w)7.5 oblique-slip earthquake occurs in the LFZ off the Pearl River Estuary(PRE),the subsequent tsunami will primarily impact Hong Kong,causing maximum positive and negative waves of around 1 m and -2 m,respectively,along with slightly destructive currents(≥1.5 m/s).An M_(w)9.0 MSZ megathrust earthquake can lead to widespread inundation with>1 m depth on the outlying islands of Macao and in the urban areas of Hong Kong around the Victoria Harbour.Besides,it will also cause catastrophic tsunami currents along the narrow waterways in Hong Kong and Macao,and the spatial distribution of strong currents(≥3 m/s)shows a considerable discrepancy from the areas of serious inundation.Thus,more attention should be paid to the potential impacts of tsunami currents on the GBA.

Support design method for deep soft-rock tunnels in non-hydrostatic high in-situ stress field

Due to the long-term plate tectonic movements in southwestern China,the in-situ stress field in deep formations is complex.When passing through deep soft-rock mass under non-hydrostatic high in-situ stress field,tunnels will suffer serious asymmetric deformation.There is no available support design method for tunnels under such a situation in existing studies to clarify the support time and support stiffness.This study first analyzed the mechanical behavior of tunnels in non-hydrostatic in-situ stress field and derived the theoretical equations of the ground squeezing curve(GSC)and ground loosening curve(GLC).Then,based on the convergence confinement theory,the support design method of deep soft-rock tunnels under non-hydrostatic high in-situ stress field was established considering both squeezing and loosening pressures.In addition,this method can provide the clear support time and support stiffness of the second layer of initial support.The proposed design method was applied to the Wanhe tunnel of the China-Laos railway in China.Monitoring data indicated that the optimal support scheme had a good effect on controlling the tunnel deformation in non-hydrostatic high in-situ stress field.Field applications showed that the secondary lining could be constructed properly.

THREE-DIMENSIONAL NON-HYDROSTATIC MODEL FOR FREE-SURFACE FLOWS WITH UNSTRUCTURED GRID

The three-dimensional Navier-Stokes equations were solved with the fractional step method where the hydrostatic pressure component was determined first, while the non-hydrostatic component of the pressure was computed from the pressure Poisson equation in which the coefficient matrix is positive definite and symmetric. The eddy viscosity was calculated from the efficient k-ε turbulence model. The resulting model is computationally efficient and unrestricted to the CFL condition. Computations with and without hydrostatic approximation were compared for the same cases to test the validity of the conventional hydrostatic pressure assumption. The model was verified against analytical solutions and experimental data, with excellent agreement.

Non-hydrostatic versus hydrostatic modelings of free surface flows

The hydrodynamics of geophysical flows in oceanic shelves, estuaries, and rivers are often studied by solving shallow water equations under either hydrostatic or non-hydrostatic assumptions. Although the hydrostatic models are quite accurate and cost-efficient for many practical applications, there are situations when the fully hydrodynamic models are preferred despite a larger cost for computations. The present numerical model is implemented by the finite volume method （FVM） based on unstructured grids. The model can be efficiently switched between hydrostatic and non-hydrostatic modules. The case study shows that for waves pro- pagating along the bar a criterion with respect to the shallowness alone, the ratio between the depth and the wave length, is insufficient to warrant the performance of shallow flow equations with a hydrostatic approach and the nonlinearity in wave dynamics can be better accounted with a hydrodynamic approach. Besides the prediction of the flows over complex bathymetries, for instance, over asymmetrical dunes, by a hydrodynamic approach is shown to be superior in accuracy to the hydrostatic simulation.

A SEMI-IMPLICIT 3-D NUMERICAL MODEL USING SIGAM-COORDINATE FOR NON-HYDROSTATIC PRESSURE FREE-SURFACE FLOWS

A 3-D numerical formulation is proposed on the horizontal Cartesian, vertical sigma-coordinate grid for modeling non-hydrostatic pressure flee-surface flows. The pressure decomposition technique and 0 semi-implicit method are used, with the solution procedure being split into two steps. First, with the implicit parts of non-hydrostatic pressures excluded, the provisional velocity field and free surface are obtained by solving a 2-D Poisson equation. Second, the theory of the differential operator is employed to derive the 3-D Poisson equation for non-hydrostatic pressures, which is solved to obtain the non-hydrostatic pressures and to update the provisional velocity field. When the non-orthogonal sigma-coordinate transformation is introduced, additional terms come into being, resulting in a 15-diagonal, diagonally dominant but unsymmetric linear system in the 3-D Poisson equation for non-hydrostatic pressures. The Biconjugate Gradient Stabilized （BiCGstab） method is used to solve the resulting 3-D unsymmetric linear system instead of the conjugate gradient method, which can only be used for symmetric, positive-definite linear systems. Three test cases are used for validations. The successful simulations of the small-amplitude wave, a supercritical flow over a ramp and a turbulent flow in the open channel indicate that the new model can simulate well non-hydrostatic flows, supercritical flows and turbulent flows.

Long-Term Integration of a Global Non-Hydrostatic Atmospheric Model on an Aqua Planet

A global non-hydrostatic atmospheric model, i.e., GRAPES_YY （Global/Regional Assimilation and Prediction System on the Yin-Yang grid）, with a semi-implicit semi-Lagrangian （SISL） dynamical core developed on the Yin-Yang grid was coupled with the physical parameterization package of the operational version of GRAPES. A 3.5-yr integration was carried out on an aqua planet to assess the numerical performance of this non-hydrostatic mo- del relative to other models. Specific aspects of precipitation and general circulation under two different sea surface temperature （SST） conditions （CONTROL and FLAT） were analyzed. The CONTROL SST peaked at the equator. The FLAT SST had its maximum gradient at about 20~ latitude, giving a broad equatorial SST maximum in the trop- ics and flat profile approaching the equator. The tropical precipitation showed different propagation features in the CONTROL and FLAT simulations. The CONTROL showed tropical precipitation bands moving eastward with some envelopes of westward convective-scale disturbance. Less organized westward-propagating rainfall cells and bands were seen in the FLAT and the propagation of the tropical wave varied with the SST gradient. The Inter Tropical Convergence Zone （ITCZ）, Hadley cell, and westerly jet core were weaker and more poleward as the SST profile flattened from the CONTROL to FLAT. The climatological structures simulated by GRAPES_YY, such as the distri- bution of precipitation and the large-scale circulation, fell within the bounds from other models. The stronger ITCZ precipitation, accompanied with stronger Hadley cells and convective heating in the CONTROL simulation, may be summed up as a result of stronger parameterized convection and the non-hydrostatic effects in GRAPES_YY. In ad- dition, mechanism of the zonal mean circulation maintaining is analyzed for the different SST patterns referring the transient eddy flux.

A HIGHER-ORDER NON-HYDROSTATIC MODEL FOR SIMULATING WAVE PROPAGATION OVER IRREGULAR BOTTOMS

A higher-order non-hydrostatic model is developed to simulate the wave propagation over irregular bottoms based on a vertical boundary-fitted coordinate system. In the model, an explicit projection method is adopted to solve the unsteady Euler equations. Advection terms are integrated explicitly with the MacCormack＇s scheme, with a second-order accuracy in both space and time. Two classical examples of surface wave propagation are used to demonstrate the capability of the model. It is found that the model with only two vertical layers could accurately simulate the motion of waves, including wave shoaling, nonlinearity, dispersion, refraction, and diffraction phenomena.

ATMOSPHERIC NON-HYDROSTATIC MODEL AND ELASTIC ADAPTATION

In this paper, various forms of non-hydrostatic model with different handling of the elastic adaptation process are analysed and compared. Some new models are suggested, among which the quasi-elastic model has the advantage of faster calculation and satisfactory accuracy.

Prediction of ship-ship interactions in ports by a non-hydrostatic model

Complicated channel geometry and currents may aggravate the interactions between passing ships and berthed ships, which should be evaluated and taken into account in a port design. A method for predicting the ship-ship interactions, based on a non-hydrostatic shallow water flow model, is presented in this paper and is validated by comparing the numerical results with experimental data. The method is subsequently applied to predict the interaction forces acting on a berthed ship due to a passing ship in ports. The influences of the difference of the water depths between the dock and the main channel, the dock geometry, the current and another berthed ship in the dock on the ship-ship interactions are studied. Analysis based on the numerical results is carried out, which is useful for the port design.

A new three-dimensional finite-volume non-hydrostatic shock-capturing model for free surface flow

In this paper a new finite-volume non-hydrostatic and shock-capturing three-dimensional model for the simulation of wave-structure interaction and hydrodynamic phenomena（wave refraction, diffraction, shoaling and breaking） is proposed. The model is based on an integral formulation of the Navier-Stokes equations which are solved on a time dependent coordinate system： a coordinate transformation maps the varying coordinates in the physical domain to a uniform transformed space. The equations of motion are discretized by means of a finite-volume shock-capturing numerical procedure based on high order WENO reconstructions. The solution procedure for the equations of motion uses a third order accurate Runge-Kutta（SSPRK） fractional-step method and applies a pressure corrector formulation in order to obtain a divergence-free velocity field at each stage. The proposed model is validated against several benchmark test cases.

Simulation of wave scattering over a floating platform in the ocean with a coupled CFD-IBM model

A numerical study of linear wave scattering over a floating platform has been simulated by an efficient numericalmodel in this letter.The non-hydrostatic model is used to simulate the free surface and the uneven bottom.For thesolid body modelling,the immersed boundary method(IBM)is implemented by introducing a virtual boundaryforce into the momentum equations to emulate the boundary conditions.This implementation enhances theability of the model to simulate interactions between waves and floating structures.A numerical case involvingwave interactions with a floating platform is studied to validate the numerical model.By simulating the wavepropagation,the numerical model captures the variation of the wave scattering very well,which verifies theperformance of the numerical model and the robust strategy of the IBM.

一次华南暴雨降水过程的模拟分析

Using a double-parameter non-hydrostatic elastic three-dimensional model with detailed microphysical processes, the authors simulate the heavy rainfall event in South China which occurred on 9 June 1998 and lasted Tor more than 3 hours. This case is a supercell, and the upward and downward drafts interact with each other, which transfers rich water vapor at the converging position to upper levels, and the two drafts together maintain the convective course. The vertical heating profiles and contributions to water matter of five kinds of micro-phase processes are revealed quantitatively in the results. Condensation releases the most heat, which is more than that of the absorption by evaporation and melting. The rain particles first come from the autoconversion of cloud particles, the warm-rain process; later from the cold-rain process, the melting of grauple particles. The precipitation intensity reaches 75 mm h?1 while its efficiency remains high. The total amount of rain is 32 mm, a value close to the observations of nearby stations.