Non-hydrostatic Dynamical Core Research Articles

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.

A Global–Regional-Unified Atmospheric Dynamical Core on the Yin–Yang Grid

Abstract A global–regional-unified nonhydrostatic dynamical core was constructed on the Yin–Yang grid using a semi-implicit semi-Lagrangian solver. Arbitrary coordinate rotation was possible for both global and limited-area models with a multilevel nesting capability. Significant flexibility is available when configuring the model’s horizontal mesh using coordinate rotation. The performance of the dynamical core was assessed using a series of numerical tests in Cartesian and spherical coordinates. The results illustrate the reasonable ability of the piecewise rational method to manage sharp gradient advection and the capability of the dry dynamical core to simulate fine structures in target systems in the Cartesian and spherical configurations. An average convergence rate of 2.43 was confirmed for the dry dynamical core in the balanced flow test. The nested grid improved the fine structure simulation of the baroclinic wave development without affecting wave propagation. The propagating speed of the vortex remained unchanged in the nested grid in the colliding modons test, although the vorticity amplitude decayed more slowly than that in the coarse grid. Proper development of topographic waves was achieved for both large- and small-scale mountains with a clear damping effect in association with the off-center semi-implicit average. A deepened trough in the nesting region, in comparison with that in the parent grid, was simulated in a topographic Rossby wave test. The implementation of coordinate rotation and grid nesting improved the numerical performance when managing atmospheric dynamical problems at relatively low cost.

Advancing precipitation prediction using a new-generation storm-resolving model framework – SIMA-MPAS (V1.0): a case study over the western United States

Abstract. Global climate models (GCMs) have advanced in many ways as computing power has allowed more complexity and finer resolutions. As GCMs reach storm-resolving scales, they need to be able to produce realistic precipitation intensity, duration, and frequency at fine scales with consideration of scale-aware parameterization. This study uses a state-of-the-art storm-resolving GCM with a nonhydrostatic dynamical core – the Model for Prediction Across Scales (MPAS), incorporated in the atmospheric component (Community Atmosphere Model, CAM) of the open-source Community Earth System Model (CESM), within the System for Integrated Modeling of the Atmosphere (SIMA) framework (referred to as SIMA-MPAS). At uniform coarse (here, at 120 km) grid resolution, the SIMA-MPAS configuration is comparable to the standard hydrostatic CESM (with a finite-volume (FV) dynamical core) with reasonable energy and mass conservation on climatological timescales. With the comparable energy and mass balance performance between CAM-FV (workhorse dynamical core) and SIMA-MPAS (newly developed dynamical core), it gives confidence in SIMA-MPAS's applications at a finer resolution. To evaluate this, we focus on how the SIMA-MPAS model performs when reaching a storm-resolving scale at 3 km. To do this efficiently, we compose a case study using a SIMA-MPAS variable-resolution configuration with a refined mesh of 3 km covering the western USA and 60 km over the rest of the globe. We evaluated the model performance using satellite and station-based gridded observations with comparison to a traditional regional climate model (WRF, the Weather Research and Forecasting model). Our results show realistic representations of precipitation over the refined complex terrains temporally and spatially. Along with much improved near-surface temperature, realistic topography, and land–air interactions, we also demonstrate significantly enhanced snowpack distributions. This work illustrates that the global SIMA-MPAS at storm-resolving resolution can produce much more realistic regional climate variability, fine-scale features, and extremes to advance both climate and weather studies. This next-generation storm-resolving model could ultimately bridge large-scale forcing constraints and better inform climate impacts and weather predictions across scales.

A nonhydrostatic atmospheric dynamical core on cubed sphere using multi-moment finite-volume method

A nonhydrostatic dynamical core has been developed by using the multi-moment finite volume method that ensures the rigorous numerical conservation of mass in this study. To represent the spherical geometry free of the polar problems, the cubed-sphere grid is adopted. A fourth-order multi-moment discretization formulation is applied to solve the governing equations cast in the local curvilinear coordinates on each patch of the cubed sphere through a gnomonic projection. In the vertical direction, the height-based terrain-following coordinate is used to deal with the topography and a finite difference scheme, also assuring the conservation of mass, is adopted for the spatial discretization. The proposed dynamical core adopts the nonhydrostatic governing equations. To get around the CFL stability restriction imposed by the sound wave and the relatively small grid spacing in the vertical direction, the dimensional splitting time integration algorithm using the HEVI (horizontally-explicit and vertically-implicit) strategy is implemented by applying the IMEX (implicit-explicit) Runge-Kutta method. The proposed model was checked by the widely-used benchmark tests in this study. The numerical results show that the multi-moment model has the comparable solution quality in comparison with the existing advanced ones and the great practical potential as a numerical platform for development of the atmospheric general circulation models.

The ICON Earth System Model Version 1.0

AbstractThis work documents the ICON‐Earth System Model (ICON‐ESM V1.0), the first coupled model based on the ICON (ICOsahedral Non‐hydrostatic) framework with its unstructured, icosahedral grid concept. The ICON‐A atmosphere uses a nonhydrostatic dynamical core and the ocean model ICON‐O builds on the same ICON infrastructure, but applies the Boussinesq and hydrostatic approximation and includes a sea‐ice model. The ICON‐Land module provides a new framework for the modeling of land processes and the terrestrial carbon cycle. The oceanic carbon cycle and biogeochemistry are represented by the Hamburg Ocean Carbon Cycle module. We describe the tuning and spin‐up of a base‐line version at a resolution typical for models participating in the Coupled Model Intercomparison Project (CMIP). The performance of ICON‐ESM is assessed by means of a set of standard CMIP6 simulations. Achievements are well‐balanced top‐of‐atmosphere radiation, stable key climate quantities in the control simulation, and a good representation of the historical surface temperature evolution. The model has overall biases, which are comparable to those of other CMIP models, but ICON‐ESM performs less well than its predecessor, the Max Planck Institute Earth System Model. Problematic biases are diagnosed in ICON‐ESM in the vertical cloud distribution and the mean zonal wind field. In the ocean, sub‐surface temperature and salinity biases are of concern as is a too strong seasonal cycle of the sea‐ice cover in both hemispheres. ICON‐ESM V1.0 serves as a basis for further developments that will take advantage of ICON‐specific properties such as spatially varying resolution, and configurations at very high resolution.

Non-Hydrostatic RegCM4 (RegCM4-NH): model description and case studies over multiple domains

Abstract. We describe the development of a non-hydrostatic version of the regional climate model RegCM4, called RegCM4-NH, for use at convection-permitting resolutions. The non-hydrostatic dynamical core of the Mesoscale Model MM5 is introduced in the RegCM4, with some modifications to increase stability and applicability of the model to long-term climate simulations. Newly available explicit microphysics schemes are also described, and three case studies of intense convection events are carried out in order to illustrate the performance of the model. They are all run at a convection-permitting grid spacing of 3 km over domains in northern California, Texas and the Lake Victoria region, without the use of parameterized cumulus convection. A substantial improvement is found in several aspects of the simulations compared to corresponding coarser-resolution (12 km) runs completed with the hydrostatic version of the model employing parameterized convection. RegCM4-NH is currently being used in different projects for regional climate simulations at convection-permitting resolutions and is intended to be a resource for users of the RegCM modeling system.

3D Convection-resolving Model of Temperate, Tidally Locked Exoplanets

Abstract A large fraction of known terrestrial-size exoplanets located in the habitable zone of M-dwarfs are expected to be tidally locked. Numerous efforts have been conducted to study the climate of such planets, using in particular 3D global climate models (GCMs). One of the biggest challenges in simulating such an extreme environment is to properly represent the effects of sub-grid convection. Most GCMs use either a simplistic convective-adjustment parameterization or sophisticated (e.g., mass flux scheme) Earth-tuned parameterizations. One way to improve the representation of convection is to study convection using numerical convection-resolving models (CRMs), with a fine spatial resolution. In this study, we developed a CRM coupling the non-hydrostatic dynamical core Advanced Research Weather-Weather Research and Forecast model with the radiative transfer and cloud/precipitation models of the Laboratoire de Météorologie Dynamique generic climate model to study convection and clouds on tidally locked planets, with a focus on Proxima b. Simulations were performed for a set of three surface temperatures (corresponding to three different incident fluxes) and two rotation rates, assuming an Earth-like atmosphere. The main result of our study is that while we recover the prediction of GCMs that (low-altitude) cloud albedo increases with increasing stellar flux, the cloud feedback is much weaker due to transient aggregation of convection leading to low partial cloud cover.

Cascading Toward a Kilometer‐Scale GCM: Impacts of a Scale‐Aware Convection Parameterization in the Goddard Earth Observing System GCM

AbstractThe National Aeronautics and Space Administration (NASA) Goddard Earth Observing System global circulation model (GCM) is evaluated through a cascade of simulations with increasing horizontal resolution. This model employs a nonhydrostatic dynamical core and includes a scale‐aware, deep convection parameterization (DPCP). The 40‐day simulations at six resolutions (100 km to 3 km) with unvarying model formulation were produced. At the highest resolution, extreme experiments were carried out: one with no DPCP and one with its scale awareness eliminated. Simulated precipitation, radiative balance, and atmospheric thermodynamic and dynamical variables are well reproduced with respect to both observational and reanalysis data. As model resolution increases, the convective precipitation smoothly transitions from being mostly produced by the convection parameterization to the cloud microphysics parameterization. However, contrary to current thought, these extreme cases argue for maintaining, to some extent, the scale‐aware DPCP even at 3‐km scale, as the run relying solely on explicit grid‐scale production of rainfall performs more poorly at this resolution.

Sensitivity of simulated temperature, precipitation, and global radiation to different WRF configurations over the Carpathian Basin for regional climate applications

In this study, the Weather Research and Forecasting (WRF) model is used to produce short-term regional climate simulations with several configurations for the Carpathian Basin region. The goal is to evaluate the performance of the model and analyze its sensitivity to different physical and dynamical settings, and input data. Fifteen experiments were conducted with WRF at 10 km resolution for the year 2013. The simulations differ in terms of configuration options such as the parameterization schemes, the hydrostatic and non-hydrostatic dynamical cores, the initial and boundary conditions (ERA5 and ERA-Interim reanalyses), the number of vertical levels, and the length of the spin-up period. E-OBS dataset 2 m temperature, total precipitation, and global radiation are used for validation. Temperature underestimation reaches 4–7 °C for some experiments and can be reduced by certain physics scheme combinations. The cold bias in winter and spring is mainly caused by excessive snowfall and too persistent snow cover, as revealed by comparison with satellite-based observations and a test simulation without snow on the surface. Annual precipitation is overestimated by 0.6–3.8 mm day−1, with biases mainly accumulating in the period driven by large-scale weather processes. Downward shortwave radiation is underestimated all year except in the months dominated by locally forced phenomena (May to August) when a positive bias prevails. The incorporation of downward shortwave radiation to the validation variables increased the understanding of underlying problems with the parameterization schemes and highlighted false model error compensations.

A Multiscale Dynamical Model in a Dry-Mass Coordinate for Weather and Climate Modeling: Moist Dynamics and Its Coupling to Physics

Abstract A multiscale dynamical model for weather forecasting and climate modeling is developed and evaluated in this study. It extends a previously established layer-averaged, unstructured-mesh nonhydrostatic dynamical core (dycore) to moist dynamics and parameterized physics in a dry-mass vertical coordinate. The dycore and tracer transport components are coupled in a mass-consistent manner, with the dycore providing time-averaged horizontal mass fluxes to passive transport, and tracer transport feeding back to the dycore with updated moisture constraints. The vertical mass flux in the tracer transport is obtained by reevaluating the mass continuity equation to ensure compatibility. A general physics–dynamics coupling workflow is established, and a dycore–tracer–physics splitting strategy is designed to couple these components in a flexible and efficient manner. In this context, two major physics–dynamics coupling strategies are examined. Simple-physics packages from the 2016 Dynamical Core Model Intercomparison Project (DCMIP2016) experimental protocols are used to facilitate the investigation of the model behaviors in idealized moist-physics configurations, including cloud-scale modeling, weather forecasting, and climate modeling, and in a real-world test-case setup. Performance evaluation demonstrates that the model is able to produce reasonable sensitivity and variability at various spatiotemporal scales. The consideration and implications of different physics–dynamics coupling options are discussed within this context. The appendix provides discussion on the energetics in the continuous- and discrete-form equations of motion.

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.

Future Directions for Whole Atmosphere Modeling: Developments in the Context of Space Weather

AbstractCoupled Sun‐to‐Earth models represent a key part of the future development of space weather forecasting. With respect to predicting the state of the thermosphere and ionosphere, there has been a recent paradigm shift; it is now clear that any self‐respecting model of this region needs to include some representation of forcing from the lower atmosphere, as well as solar and geomagnetic forcing. Here we assess existing modeling capability and set out a road map for the important next steps needed to ensure further advances. These steps include a model verification strategy, analysis of the impact of nonhydrostatic dynamical cores, and a cost‐benefit analysis of model chemistry for weather and climate applications.

Comparison of Simulated Tropical Cyclone Intensity and Structures Using the WRF with Hydrostatic and Nonhydrostatic Dynamical Cores

This study explored the influence of choosing a nonhydrostatic dynamical core or a hydrostatic dynamical core in the weather research and forecasting (WRF) model on the intensity and structure of simulated tropical cyclones (TCs). A comparison of cloud-resolving simulations using each core revealed significant differences in the TC simulations. In comparison with the nonhydrostatic simulation, the hydrostatic simulation produced a stronger and larger TC, associated with stronger convective activity. A budget analysis of the vertical momentum equation was conducted to investigate the underlying mechanisms. Although the hydrostatic dynamical core was used, the vertical motion was not in strict hydrostatic balance because of the existence of the vertical perturbation pressure gradient force, local buoyancy force, water loading, and sum of the Coriolis and diffusion effects. The contribution of the enhanced vertical perturbation pressure gradient force was found to be more important for stronger upward acceleration in the eyewall in the hydrostatic simulation than in the nonhydrostatic simulation. This is because it leads to intensified convection in the eyewall that releases more latent heat, which induces a larger low-level radial pressure gradient and inflow motion, and eventually leads to a stronger storm.

The Korean Integrated Model (KIM) System for Global Weather Forecasting

The Korea Institute of Atmospheric Prediction Systems (KIAPS) began a national project to develop a new global atmospheric model system in 2011. The ultimate goal of this 9-year project is to replace the current operational model at the Korea Meteorological Administration (KMA), which was adopted from the United Kingdom’s Meteorological Office’s unified model (UM) in 2010. The 12-km Korean Integrated Model (KIM) system, consisting of a spectral-element non-hydrostatic dynamical core on a cubed sphere grid and a state-of-the-art physics parameterization package, has been launched in a real-time forecast framework, with initial conditions obtained via the advanced hybrid four-dimensional ensemble variational data assimilation (4DEnVar) over its native grid. A development strategy for KIM and the evolution of its performance in medium-range forecasts toward a world-class global forecast system are described. Outstanding issues in KIM 3.1 as of February 2018 are discussed, along with a future plan for operational deployment in 2020.

DCMIP2016: a review of non-hydrostatic dynamical core design and intercomparison of participating models

Abstract. Atmospheric dynamical cores are a fundamental component of global atmospheric modeling systems and are responsible for capturing the dynamical behavior of the Earth's atmosphere via numerical integration of the Navier–Stokes equations. These systems have existed in one form or another for over half of a century, with the earliest discretizations having now evolved into a complex ecosystem of algorithms and computational strategies. In essence, no two dynamical cores are alike, and their individual successes suggest that no perfect model exists. To better understand modern dynamical cores, this paper aims to provide a comprehensive review of 11 non-hydrostatic dynamical cores, drawn from modeling centers and groups that participated in the 2016 Dynamical Core Model Intercomparison Project (DCMIP) workshop and summer school. This review includes a choice of model grid, variable placement, vertical coordinate, prognostic equations, temporal discretization, and the diffusion, stabilization, filters, and fixers employed by each system.

Colliding Modons: A Nonlinear Test for the Evaluation of Global Dynamical Cores

AbstractThe modon, a pair of counter‐rotating vortices propelling one another along a straight line, is an idealization of some observed large‐scale and small‐scale atmospheric and oceanic processes (e.g., twin cyclones), providing a challenging nonlinear test for fluid‐dynamics solvers (known as “dynamical cores”). We present an easy‐to‐setup test of colliding modons suitable for both shallow‐water and three‐dimensional dynamical cores on the sphere. Two pairs of idealized modons are configured to collide, exchange vortices, and depart in opposite directions, repeating indefinitely in the absence of ambient rotation. This test is applicable to both hydrostatic and nonhydrostatic dynamical cores and is particularly challenging for refined grids on the sphere, regardless of solution methodology, or vertical coordinate. We applied this test to three popular dynamical cores, used by three different general circulation models: the Spectral‐Element (SE) core of the Community Atmosphere Model, the Geophysical Fluid Dynamics Laboratory (GFDL) spectral core, and the GFDL Finite‐Volume Cubed‐Sphere dynamical core (FV3). Tests with a locally refined grid and nonhydrostatic dynamics were also performed with FV3. All cores tested were able to capture the propagation, collision, and exchange of the modons, albeit the rate at which the modon was diffused varied between the three cores and showed a strong dependence on the strength of hyperdiffusion.

Numerical Effects on Wave Propagation in Atmospheric Models

AbstractRay tracing techniques have been used to investigate numerical effects on the propagation of acoustic waves in a non-hydrostatic dynamical core discretised using an Arakawa C-grid horizontal staggering of variables (Arakawa & Lamb 1977) and a Charney-Phillips vertical staggering of variables (Charney & Phillips 1953) with a semi-implicit timestepping scheme. It is found that the space discretisation places limits on resolvable wavenumbers and redirects the group velocity of waves towards the vertical. Wave amplitudes grow exponentially with height due to the decrease in the background density, which can cause instabilities in whole-atmosphere models. However, the inclusion of molecular viscosity and diffusion acts to damp the exponential growth of waves above about 150 km. This study aims to demonstrate the extent to which numerical wave propagation causes instabilities at high altitudes in atmosphere models, and how processes that damp the waves can improve these model’s stability.

Exploring the effects of a nonhydrostatic dynamical core in high‐resolution aquaplanet simulations

AbstractThis study explores the impact of a nonhydrostatic dynamical core in high‐resolution regional climate simulations using an aquaplanet framework. The Weather Research and Forecasting (WRF) model is used to conduct simulations with both hydrostatic (H) and nonhydrostatic (NH) solvers at horizontal grid spacings (Δx) of 36, 12, and 4 km. The differences between the H and NH simulated precipitation (ΔP) are notable even at Δx = 12 km in the intertropical convergence zone and the transition region to the drier subtropics. At gray zone grid spacing (12 km and 4 km) over the tropics, ΔP is sensitive to whether a cumulus parameterization scheme is used or not. With an idealized Witch of Agnesi land mountain, differences in the precipitation and circulation (vertical velocity) between the H and NH simulations are significant even at Δx = 36 km in the tropics due largely to the strong feedbacks related to moist processes. The differences increase as the model grid spacing and mountain half width (a) are reduced, accompanied by a shift toward a more nonhydrostatic flow regime at a = 24 km. Latent heat release drastically enhances the differences between the NH and H simulations and extends the effect of nonhydrostatic dynamics to a broader region over the mountain and downstream over the tropics. Overall, differences exist between H and NH simulations even at resolutions between 12 and 36 km, but the differences are sensitive to the representations of moist physics and other features such as horizontal diffusion used in the WRF model.

Comparison of Simulated Precipitation over East Asia in Two Regional Models with Hydrostatic and Nonhydrostatic Dynamical Cores

AbstractThis study examines the characteristics of a nonhydrostatic dynamical core compared to a corresponding hydrostatic dynamical core in the Regional Model Program (RMP) of the Global/Regional Integrated Model system (GRIMs), a spectral model for regional forecasts, focusing on simulated precipitation over Korea. This kind of comparison is also executed in the Weather Research and Forecasting (WRF) finite-difference model with the same physics package used in the RMP. Overall, it is found that the nonhydrostatic dynamical core experiment accurately reproduces the heavy rainfall near Seoul, South Korea, on a 3-km grid, relative to the results from the hydrostatic dynamical core in both models. However, the characteristics of nonhydrostatic effects on the simulated precipitation differ between the RMP and WRF Model. The RMP with the nonhydrostatic dynamical core improves the local maximum, which is exaggerated in the hydrostatic simulation. The hydrostatic simulation of the WRF Model displaces the major precipitation area toward the mountainous region along the east coast of the peninsula, which is shifted into the observed area in the nonhydrostatic simulation. In the simulation of a summer monsoonal rainfall, these nonhydrostatic effects are negligible in the RMP, but the simulated monsoonal rainfall is still influenced by the dynamical core in the WRF Model even at a 27-km grid spacing. One of the reasons for the smaller dynamical core effect in the RMP seems to be the relatively strong horizontal diffusion, resulting in a smaller grid size of the hydrostatic limit.

50th anniversary of Numerical Weather Prediction (NWP) in the UK

50th anniversary of Numerical Weather Prediction (<scp>NWP</scp>) in the <scp>UK</scp>