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DOE OSTI2025

A nonhydrostatic formulation for MPAS-Ocean

The Model for Prediction Across Scales-Ocean (MPAS-Ocean) is an open-source, global ocean model and is one component of a family of climate models within the MPAS framework, including atmosphere, sea-ice, and land-ice models. Here, in this work, a new formulation for the ocean model is presented that solves the nonhydrostatic, incompressible Boussinesq equations on an unstructured, staggered, z-level grid. The introduction of this nonhydrostatic capability is necessary for the resolution of internal wave dynamics and large eddy simulations. Compared to the standard, hydrostatic formulation, a nonhydrostatic pressure solver and a vertical momentum equation are added, where the PETSc (Portable Extensible Toolkit for Scientific Computation) library is used for the inversion of a large sparse system for the nonhydrostatic pressure. Numerical results on a stratified seiche, internal solitary wave, overflow and lock-exchange test cases are presented, and the parallel efficiency of the code is evaluated using up to 1024 processors.

3D Poisson equation↗

DOE OSTI2025

A nonhydrostatic formulation for MPAS-Ocean

3D Poisson equation↗

NASA NTRS1993

Nonhydrostatic effects in numerical modeling of mesoscale convective systems and baroclinic waves

The present investigation is concerned with the role of convection upon mesoscale modeling results, particularly when the grid resolution becomes small enough that there is not a clear scale separation between the explicitly resolved circulations and the parameterized clouds. In those situations, the vertical accelerations in explicitly resolved circulations become strong enough that the hydrostatic assumption may no longer be valid. These concerns arise from interests in improving mesoscale modeling per se and in improving the subgrid-scale parameterizations in global models. The hydrostatic and the nonhydrostatic options of the Colorado State University Regional Atmospheric Modeling System were used to simulate dry gravity currents in two dimensions, using several different horizontal grid sizes. With horizontal grid intervals of 10 km or less, nonhydrostatic simulations produce wider and colder heads and weaker but wider forced updrafts than do the hydrostatic simulations. Comparing the hydrostatic and nonhydrostatic models show that the difference between the vertical mass fluxes is much less than the difference between the vertical velocities. When the grid is fine enough to resolve the head of the gravity current, horizontal convergence at the gust front extends upwards almost to the head of the cold air. Vertical mass flux in the forced updraft at the front varies with horizontal grid size mainly as a function of the height of the simulated head. For coarser grids, which do not resolve the head, vertical mass flux at all heights decreases with increasing horizontal grid size. A comparison on nonhydrostatic simulations with horizontal grid intervals of 1 km and 2 km illustrates how decreasing the grid size does not necessarily increase the intensity of the resolved circulation. The smaller grid enables the simulated gravity current to entrain a bubble of warm air behind the head, which results in a weaker circulation with a shorter head and weaker updraft.

Cohen, Charles↗

DOE OSTI2024

Energy-conserving physics for nonhydrostatic dynamics in mass coordinate models

Abstract. Motivated by reducing errors in the energy budget related to enthalpy fluxes within the Energy Exascale Earth System Model (E3SM), we study several physics–dynamics coupling approaches. Using idealized physics, a moist rising bubble test case, and the E3SM's nonhydrostatic dynamical core, we consider unapproximated and approximated thermodynamics applied at constant pressure or constant volume. With the standard dynamics and physics time-split implementation, we describe how the constant-pressure and constant-volume approaches use different mechanisms to transform physics tendencies into dynamical motion and show that only the constant-volume approach is consistent with the underlying equations. Using time step convergence studies, we show that the two approaches both converge but to slightly different solutions. We reproduce the large inconsistencies between the energy flux internal to the model and the energy flux of precipitation when using approximate thermodynamics, which can only be removed by considering variable latent heats, both when computing the latent heating from phase change and when applying this heating to update the temperature. Finally, we show that in the nonhydrostatic case, for physics applied at constant pressure, the general relation that enthalpy is locally conserved no longer holds. In this case, the conserved quantity is enthalpy plus an additional term proportional to the difference between hydrostatic pressure and full pressure.

58 GEOSCIENCES↗

NASA NTRS1993

A nonreflecting upper boundary condition for anelastic nonhydrostatic mesoscale gravity-wave models

A sponge layer is formulated to prevent spurious reflection of vertically propagating quasi-stationary gravity waves at the upper boundary of a two-dimensional numerical anelastic nonhydrostatic model. The sponge layer includes damping of both Newtonian-cooling type and Rayleigh-friction type, whose coefficients are determined in such a way that the reflectivity of wave energy at the bottom of the layer is zero. Unlike the formulations in earlier studies, our formulation includes the effects of vertical discretization, vertical mean density variation, and nonhydrostaticity. This sponge formulation is found effective in suppressing false downward reflection of waves for various types of quasi-stationary forcing.

Kim, Young-Joon↗

NASA NTRS1993

A nonhydrostatic version of the Penn State-NCAR Mesoscale Model - Validation tests and simulation of an Atlantic cyclone and cold front

A nonhydrostatic extension to the Pennsylvania State University-NCAR Mesoscale Model is presented, which employs reference pressure as the basis for a terrain-following vertical coordinate, and the fully compressible system of equations. It is shown that this model, combined with the existing initialization techniques and the physics of the current hydrostatic model, is capable of real-data simulations on any scale, limited only by data quality and resolution and by computer resources. An example of an explosive cyclone simulation is presented, demonstrating the capability of the nonhydrostatic model to reproduce the hydrostatic model results at large scales.

Dudhia, Jimy↗

DOE OSTI2022

An Assessment of Nonhydrostatic and Hydrostatic Dynamical Cores at Seasonal Time Scales in the Energy Exascale Earth System Model (E3SM)

Abstract In global atmospheric modeling, the differences between nonhydrostatic (NH) and hydrostatic (H) dynamical cores are negligible in dry simulations when grid spacing is larger than 10 km. However, recent studies suggest that those differences can be significant at far coarser resolution when moisture is included. To better understand how NH and H differences manifest in global fields, we perform and analyze an ensemble of 28 and 13 km seasonal simulations with the NH and H dynamical cores in the Energy Exascale Earth System Model global atmosphere model, where the differences between H and NH configurations are minimized. A set of idealized rising bubble experiments is also conducted to further investigate the differences. Although NH and H differences are not significant in global statistics and zonal averages, significant differences in precipitation amount and patterns are observed in parts of the tropics. The most prominent differences emerge near India and the Western Pacific in the boreal summer, and the central‐southern Indian Ocean and Pacific in the boreal winter. Tropical differences influence surrounding regions through modification of the regional circulation and can propagate to the extratropics, leading to significant temperature and geopotential differences over the middle to high latitudes. While the dry bubble experiments show negligible deviation between H and NH dynamics until grid spacing is below 6.25 km, precipitation amount and vertical velocity are different in the moist case even at 25 km resolution.

58 GEOSCIENCES↗

DOE OSTI2019

An Energy Consistent Discretization of the Nonhydrostatic Equations in Primitive Variables

We derive a formulation of the nonhydrostatic equations in spherical geometry with a Lorenz staggered vertical discretization. The combination conserves a discrete energy in exact time integration when coupled with a mimetic horizontal discretization. The formulation is a version of Dubos and Tort (2014, https://doi.org/10.1175/MWR-D-14-00069.1) rewritten in terms of primitive variables. It is valid for terrain following mass or height coordinates and for both Eulerian or vertically Lagrangian discretizations. The discretization relies on an extension to Simmons and Burridge (1981, https://doi.org/10.1175/1520-0493(1981)109<0758:AEAAMC>2.0.CO;2) vertical differencing, which we show obeys a discrete derivative product rule. This product rule allows us to simplify the treatment of the vertical transport terms. Energy conservation is obtained via a term-by-term balance in the kinetic, internal, and potential energy budgets, ensuring an energy-consistent discretization up to time truncation error with no spurious sources of energy. We demonstrate convergence with respect to time truncation error in a spectral element code with a horizontal explicit vertically implicit implicit-explicit time stepping algorithm.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Precipitation Characteristics and Future Changes Over the Southern Slope of Tibetan Plateau Simulated by a High-Resolution Global Nonhydrostatic Model

Current climate model resolution cannot accurately describe the complex topography over the Tibetan Plateau, which limits our understanding of past and future precipitation over this region. This study investigates the daily precipitation characteristics and its future changes over the Tibetan Plateau, especially for the southern slope of Tibetan Plateau (SSTP), by 14-km Nonhydrostatic ICosahedral Atmospheric Model (NICAM) with explicitly calculated convection for historical and future 30-years period. By comparing with the satellite Global Precipitation Measurement (GPM), NICAM well reproduces the historical precipitation spatial pattern, seasonal cycle, and the extreme precipitation belt over SSTP, but overestimates precipitation amount by~35%. It is found that heavy precipitation probability decreases as elevation becomes higher while the light precipitation generally shows the opposite. For the precipitation changes during June to September from 1979–2008 to 2075–2104, NICAM predicts that mean precipitation will decrease over low-level SSTP but increase over high-level SSTP. Nonprecipitation and heavy precipitation probability will increase while light precipitation probability will decrease in the future over SSTP. The extreme precipitation probability and intensity will increase ~50%/°C and ~8%/°C over SSTP, and this increase is more obvious as elevation becomes higher. The robust increase of extreme precipitation along the SSTP topography is unique and has not been identified by the climate model simulations before. The strong meridional gradient of specific humidity over SSTP is found to be further enhanced under global warming, and this gradient enhancement is suggested to be responsible for the increase in the extreme precipitation over SSTP.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Mesoscale Convective Systems Simulated by a High–Resolution Global Nonhydrostatic Model Over the United States and China

Mesoscale convective systems (MCSs) contribute a large fraction of warm-season precipitation and generate hazardous weather with substantial socio-economic impacts. Uncertainties in convection parameterizations in climate models limit our understanding of MCS characteristics and reliability of future projection. We examine the MCS simulation from the global 14-km Nonhydrostatic ICosahedral Atmospheric Model (NICAM) without cumulus parameterization against satellite observation from Global Precipitation Measurement (GPM) during 2001-2008. We focus on MCSs over the central U.S. and eastern China where MCSs prevail from March to August. A process-oriented tracking method incorporating both cloud and precipitation criteria is used to identify and track MCSs. About 140/100 MCSs initiate in the central U.S./eastern China per warm season and most of them initiate east of high mountains and in coastal regions. The frequency distribution of MCS lifetime is well captured in NICAM. But the simulated MCSs have stronger precipitation, smaller precipitation area, and larger cold cloud system than observed in both regions, which may be caused by weak entrainment as it is not well resolved at 14 km resolution. Here, the simulated MCS number is also underestimated in summer. By examining the climatological and MCS large-scale environments, the significant underestimation of MCS number in summer over the central U.S. may be attributed to the large climatological dry bias in the atmosphere. For China, mean moisture in summer is well simulated but deficiency in capturing the dynamic condition related to the coastal topography for triggering convection may have contributed to underestimation of MCS even in a sufficiently moist environment.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1977

The multiple nesting of mesoscale, submesoscale, and nonhydrostatic microscale numerical models for a case of mesocyclogenesis and severe storm development

A fundamental approach involving the integration of two different numerical models over several different spatial mesh lengths is considered. Model I is a hydrostatic, incompressible, and adiabatic primitive (Newtonian) equation set with no boundary layer forcing, i.e., surface heat or moisture flux or external frictional stresses. Typically this model is initialized from conventional radiosonde data and run for a 12-15 hour forecast period over a 40 km horizontal mesh. If phase I of the tornado developmental processes develops, the data is 'frozen' in space and time, interpolated to a 20 km mesh, and integrated for a shorter time period (3 hours) with a shorter time step. Model II is a nonhydrostatic compressible 18-level complement of model I. If model II indicates the development of the intensification of phase V dynamical processes, the data is frozen and interpolated to finer mesh lengths until the tornadic circulation system is approximated

Kaplan, M. L.↗

NASA NTRS1985

Application of radiative boundary conditions to nonhydrostatic primitive equation models

A procedure is presented for applying a radiative boundary condition to the lateral boundary of a limited domain model. The model considered, the Terminal Area Simulation System (TASS), has nonhydrostatic compressible and unsteady governing equations. The primary applications to date have been studies of downbursts, wind shear, thunderstorms and mass fires. A time-splitting integration is used with TASS, with the acoustic terms being integrated separately with a smaller time step. A first-order closure approximation is employed to ensure subgrid turbulence closure. TASS applications for two-dimensional axisymmetric and three-dimensional simulations are described. The radiative boundary conditions were applied in the two-dimensional case to the temperature, pressure and non-normal velocity components. Solutions in both cases avoided runaway circulations and experienced minimal domain-wide mass loss. Also, distorsion was minimized at the boundaries.

Proctor, F. H.↗

NASA NTRS1991

The effects of the solid inner core and nonhydrostatic structure on the earth's forced nutations and earth tides

This paper computes the effects of the solid inner core (IC) on the forced nutations and earth tides, and on certain of the earth's rotational normal modes. The theoretical results are extended to include the effects of a solid IC and of nonhydrostatic structure. The presence of the IC is responsible for a new, almost diurnal, prograde normal mode which involves a relative rotation between the IC and fluid outer core about an equatorial axis. It is shown that the small size of the IC's effects on both nutations and tides is a consequence of the fact that the IC's moments of inertia are less than 1/1000 of the entire earth's.

De Vries, Dan↗

NASA NTRS1991

A nested grid, nonhydrostatic, elastic model using a terrain-following coordinate transformation - The radiative-nesting boundary conditions

This study presents a nested-grid nonhydrostatic and elastic model using a terrain-following coordinate transformation as well as a unique application of grid-nesting techniques to the time-splitting elastic model. A simulation of the 10-m-high Witch of Agnesi Mountain provides the control to test this new model. The results show that the model produces the same solution as that derived from a simple linear analytic model. It is demonstrated that the new nested-grid model improves model resolution without resorting to the costly method of placing a fine-resolution grid over the entire domain. Since the wave reflection from the boundaries of the fine-grid model is well controlled, the boundary of the nested fine-grid model can be located even at the wave-active region. The model can be used to simulate various weather systems in which scale interactions are important.

Chen, Chaing↗

NASA NTRS1992

An explicit three-dimensional nonhydrostatic numerical simulation of a tropical cyclone

A nonhydrostatic numerical simulation of a tropical cyclone is performed with explicit representation of cumulus on a meso-beta scale grid and for a brief period on a meso-gamma scale grid. Individual cumulus plumes are represented by a combination of explicit resolution and a 1.5 level closure predicting turbulent kinetic energy (TKE).

Tripoli, G. J.↗

NASA NTRS2017

Description and Evaluation of the Multiscale Online Nonhydrostatic AtmospheRe CHemistry Model (NMMB-MONARCH) Version 1.0: Gas-Phase Chemistry at Global Scale

This paper presents a comprehensive description and benchmark evaluation of the tropospheric gas-phase chemistry component of the Multiscale Online Nonhydrostatic AtmospheRe CHemistry model (NMMBMONARCH), formerly known as NMMB/BSC-CTM, that can be run on both regional and global domains. Here, we provide an extensive evaluation of a global annual cycle simulation using a variety of background surface stations (EMEP, WDCGG and CASTNET), ozonesondes (WOUDC, CMD and SHADOZ), aircraft data (MOZAIC and several campaigns), and satellite observations (SCIAMACHY and MOPITT).We also include an extensive discussion of our results in comparison to other state-of-the-art models. We note that in this study, we omitted aerosol processes and some natural emissions (lightning and volcano emissions). The model shows a realistic oxidative capacity across the globe. The seasonal cycle for CO is fairly well represented at different locations (correlations around 0.3-0.7 in surface concentrations), although concentrations are underestimated in spring and winter in the Northern Hemisphere, and are overestimated throughout the year at 800 and 500 hPa in the Southern Hemisphere. Nitrogen species are well represented in almost all locations, particularly NO2 in Europe (root mean square error - RMSE - below 5 ppb). The modeled vertical distributions of NOx and HNO3 are in excellent agreement with the observed values and the spatial and seasonal trends of tropospheric NO2 columns correspond well to observations from SCIAMACHY, capturing the highly polluted areas and the biomass burning cycle throughout the year. Over Asia, the model underestimates NOx from March to August, probably due to an underestimation of NOx emissions in the region. Overall, the comparison of the modeled CO and NO2 with MOPITT and SCIAMACHY observations emphasizes the need for more accurate emission rates from anthropogenic and biomass burning sources (i.e., specification of temporal variability).

atmospheric chemistry↗

NASA NTRS2021

Mineral Dust Cycle in the Multiscale Online Nonhydrostatic AtmospheRe CHemistry Model (Monarch) Version 2.0

We present the dust module in the Multiscale Online Non-hydrostatic AtmospheRe CHemistry model (MONARCH) version 2.0, a chemical weather prediction system that can be used for regional and global modeling at a range of resolutions. The representations of dust processes in MONARCH were upgraded with a focus on dust emission (emission parameterizations, entrainment thresholds, considerations of soil moisture and surface cover), lower boundary conditions (roughness, potential dust sources), and dust–radiation interactions. MONARCH now allows modeling of global and regional mineral dust cycles using fundamentally different paradigms, ranging from strongly simplified to physics-based parameterizations. We present a detailed description of these updates along with four global benchmark simulations, which use conceptually different dust emission parameterizations, and we evaluate the simulations against observations of dust optical depth. We determine key dust parameters, such as global annual emission/deposition flux, dust loading, dust optical depth, mass-extinction efficiency, single-scattering albedo, and direct radiative effects. For dust-particle diameters up to 20 µm, the total annual dust emission and deposition fluxes obtained with our four experiments range between about 3500 and 6000 Tg, which largely depend upon differences in the emitted size distribution. Considering ellipsoidal particle shapes and dust refractive indices that account for size-resolved mineralogy, we estimate the global total (longwave and shortwave) dust direct radiative effect (DRE) at the surface to range between about −0.90 and −0.63 W m−2 and at the top of the atmosphere between −0.20 and −0.28 W m−2. Our evaluation demonstrates that MONARCH is able to reproduce key features of the spatiotemporal variability of the global dust cycle with important and insightful differences between the different configurations.

Dust cycle↗

DOE OSTI2023

The Flux-Differencing Discontinuous Galerkin Method Applied to an Idealized Fully Compressible Nonhydrostatic Dry Atmosphere

Dynamical cores used to study the circulation of the atmosphere employ various numerical methods ranging from finite-volume, spectral element, global spectral, and hybrid methods. In this work, we explore the use of Flux-Differencing Discontinuous Galerkin (FDDG) methods to simulate a fully compressible dry atmosphere at various resolutions. We show that the method offers a judicious compromise between high-order accuracy and stability for large-eddy simulations and simulations of the atmospheric general circulation. In particular, filters, divergence damping, diffusion, hyperdiffusion, or sponge-layers are not required to ensure stability; only the numerical dissipation naturally afforded by FDDG is necessary. We apply the method to the simulation of dry convection in an atmospheric boundary layer and in a global atmospheric dynamical core in the standard benchmark of Held and Suarez

54 ENVIRONMENTAL SCIENCES↗