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.

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.

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.

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.

A methodology for lining design of circular mine shafts in different rock masses

In this study, the finite element numerical modelling of 2D shaft sections in a Hoek–Brown medium are carried out in a non-hydrostatic stress state in an attempt to predict pressures developing around mine shafts. An iterative process of applying support pressure until observing no failure zone around the shaft is used to simulate the required lining support pressure for different shaft models. Later, regression analysis is carried out to find a generic shaft pressure equation representing the rock mass and the stress state. Finally, the developed pressure equation which shows a good agreement with a case study is used in elastic ‘‘thick-walled cylinder" equation to calculate the lining thickness required to prevent the development of a failure zone around the shaft. At the end of the study, a user-friendly object-oriented computer program ‘‘Shaft 2D" is developed to simplify the rigorous shaft lining thickness calculation process.

An Efficient Hydrodynamic Model for Surface Waves

In the present study, a semi-implicit finite difference model for non-hydrostatic, free-surface flows is analyzed and discussed. The governing equations are the three-dimensional free-surface Reynolds-averaged Navier-Stokes equations defined on a general, irregular domain of arbitrary scale. At outflow, a combination of a sponge layer technique and a radiation boundary condition is applied to minimize wave reflection. The equations are solved with the fractional step method where the hydrostatic pressure component is determined first, while the non-hydrostatic component of the pressure is computed from the pressure Poisson equation in which the coefficient matrix is positive definite and symmetric. The advection and horizontal viscosity terms are discretized by use of a semi-Lagrangian approach. The resulting model is computationally efficient and unrestricted to the CFL condition. The developed model is verified against analytical solutions and experimental data, with excellent agreement.

Three dimensional simulation of internal wave attractors in the Luzon Strait

Internal waves propagate along wave beams that are inclined with respect to the horizontal plane. It is conjectured that the internal waves generated in the Luzon Strait may be confined between the double ridges in the strait and concentrate to a closed trajectory, the so-called internal wave attractor, due to the reflection of wave beams from the lateral boundaries, sea surface and bottom. This work carried out two experiments using a three dimensional non-hydrostatic general circulation model, MITgcm, to investigate the possibility that the ridges in the Lnzon Strait allows for internal wave attractors. Baroclinic current in both of the experiments demonstrate the forming of ring-like patterns in some section around 20° and 21°N, indicating that the development of the internal wave attractors are allowed in the Luzon Strait. The different resolutions and initial conditions in the two experiments also reveal that the internal-wave-attractor phenomenon is robust in this region.

Ruby fluorescence pressure scale: Revisited

Effect of non-hydrostatic stress on X-ray diffraction in a diamond anvil cell （DAC） is studied. The pressure gradient in the sample chamber leads to the broadening of the diffraction peaks, which increase with the hkl index of the crystal. It is found that the difference between the determined d-spacing compressive ratio d/do and the real d-spacing compressive ratio dr/do is determined by the yield stress of the pressure transmitting media （if used） and the shear modulus of the sample. On the basis of the corrected experiment data of Mao et al. （MXB86）, which was used to calibrate the most widely used ruby fluorescence scale, a new relationship of ruby fluorescence pressure scale is corrected, i.e., P = （1904/9.827）[（1 ＋ △λ/λ0）9.827 - 1].