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The non‐hydrostatic Model for Prediction Across Scales‐Atmosphere (MPAS‐A) dynamical core has recently been adapted for the Specified Chemistry Whole Atmosphere Community Climate Model (SC‐WACCM). In this study, the mean zonal wind and temperature climatology from SC‐WACCM/MPAS‐A is compared with the results from SC‐WACCM using the finite volume and spectral element dynamical cores, as well as the zonal wind and temperature climatology of Upper Atmosphere Research Satellite mission and SABER. The simulations have been performed at horizontal resolutions of ∼100 km. Generally a good agreement is seen between the results from the three dynamical cores, which verifies that the new dynamical core is working with WACCM. Plain Language Summary Development of whole atmosphere models are focusing increasingly more on geospace applications. This focus stems from our society becoming dependent on advanced technology which can be vulnerable to space weather. In these regions the accuracy of the hydrostatic approximation becomes problematic. In this work the Whole Atmosphere Community Climate Model at the National Center for Atmospheric Research is developed and tested with the non‐hydrostatic Model for Prediction Across Scales‐Atmosphere dynamical core. Key Points Whole Atmosphere Community Climate Model (WACCM) with the non‐hydrostatic Model for Prediction Across Scales‐Atmosphere (MPAS‐A) dynamical core has been developed Temperature and wind climatology from WACCM/MPAS‐A is compared with results from the spectral element (SE) and finite volume (FV) dynamical cores, as well as available observations Preliminary validation demonstrates agreement with the result from the SE and FV dynamical cores

This paper provides a comprehensive derivation of the total energy equations for the atmospheric components of Earth System Models (ESMs). The assumptions and approximations made in this derivation are motivated and discussed. In particular, it is emphasized that closing the energy budget is conceptually challenging and hard to achieve in practice without resorting to ad hoc fixers. As a concrete example, the energy budget terms are diagnosed in a realistic climate simulation using a global atmosphere model. The largest total energy errors in this example are spurious dynamical core energy dissipation, thermodynamic inconsistencies (e.g., coupling parameterizations with the host model) and missing processes/terms associated with falling precipitation and evaporation (e.g., enthalpy flux between components). The latter two errors are not, in general, reduced by increasing horizontal resolution. They are due to incomplete thermodynamic and dynamic formulations. Future research directions are proposed to reconcile and improve thermodynamics formulations and conservation principles. Plain Language Summary Earth System Models (ESMs) have numerous total energy budget errors. This article establishes the governing total energy equations for large‐scale ESMs and assesses the energy budget errors in real‐world simulations in a widely used climate model. To move towards a closed energy budget in ESMs, further research on total energy conserving discretizations (in the dynamical core), unified thermodynamics (through thermodynamic potentials/conserved variables) and missing processes is paramount. This research is especially important since some of the energy budget errors will not improve with higher spatial resolution and may even get worse. Key Points Closing total energy budgets in Earth System Models without ad hoc fixers is a monumental task Largest errors are from missing processes/terms, thermodynamic inconsistencies and dynamical core Further research is needed on conservative discretizations, unified thermodynamics and missing processes

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. Plain Language Summary Energy consistent discretizations have proven useful in guiding the development of numerical methods for simulating fluid dynamics. They ensure that the discrete method does not have any spurious sources of energy, which can lead to unstable and unrealistic simulations. Here we provide an energy consistent discretization of the equations used by global models of the Earth's atmosphere. The discretization is written in terms of standard variables in spherical coordinates and supports a wide variety of terrain following vertical coordinates. It can be used with any horizontal discretization that has a discrete version of the integration‐by‐parts identity. Key Points We give a discrete Hamiltonian formulation of the nonhydrostatic equations in primitive variables The formulation supports mass or height terrain following coordinates The Lorenz staggered vertical discretization obeys a derivative product rule

The gnomonic cubed‐sphere grid has excellent accuracy and uniformity, but the “kink” in the coordinates at the cube edges in the halo region can leave an imprint of the cube in the solution, and requires special edge handling. To reduce grid imprinting, we implement the novel “Duo‐Grid” within the Geophysical Fluid Dynamics Laboratory's (GFDL) Finite‐Volume Cubed‐Sphere Dynamical Core (FV3). The Duo‐Grid remaps a cube face's data from neighboring face from kinked to natural locations along great circle lines using 1D piecewise linear interpolation. A 2D interpolation algorithm is used to fill correct data at the eight corners of the cubed‐sphere needed for FV3's 2D advection scheme. The Duo‐Grid was tested in idealized tests using the 2D shallow water solver and the 3D hydrostatic and non‐hydrostatic solvers. We found that error norms are greatly reduced and grid imprinting is practically eliminated when employing the Duo‐Grid. These results indicate that FV3's accuracy and robustness have improved. Plain Language Summary In Computational Fluid Dynamics (CFD), numerical solutions should ideally be grid‐independent, so that grid choice should have no noticeable effects on flow behavior. However, designing complex CFD codes in general and atmospheric dynamical cores in particular necessitates a series of design decisions that balance the code numerical efficiency and accuracy. In GFDL's dynamical core FV3, unphysical structures from the gnomonic cubed‐sphere grid structure, such as edges and corners, can appear in the numerical solution especially at lower resolutions and in long climate simulations. This is known as grid imprinting which is due to errors in the assumed location of grid cells on opposing sides of a cube edge. While this assumption is computationally inexpensive, it creates a grid imprinting problem especially for low resolution simulations. In this paper, we implement a new algorithm called Duo‐Grid that corrects the location of the cross‐edge data, and eliminates grid imprinting in FV3. The increase in accuracy comes at the expense of additional computational complexity. Key Points A new cubed‐sphere grid structure, the “Duo‐Grid,” is implemented in the Geophysical Fluid Dynamics Laboratory's Dynamical Core (FV3) The Duo‐Grid remaps data along cube edges and synchronizes fluxes to rectify the “kink” in the coordinates Grid imprinting of the cubed sphere is greatly reduced in idealized tests and FV3's accuracy and robustness have improved

This study discusses the computational advantages of high-order dynamical cores over a conventional low-order dynamical core in atmospheric turbulent simulations. Implicit and explicit large-eddy simulations (LES) of dry Rayleigh convection were performed using two dynamical cores: one based on a high-order discontinuous Galerkin method (DGM) and the other on a totally second-order conventional finite-volume method (FVM) with advection schemes of various orders. The effective resolution and numerical energy accumulation, derived from kinetic energy spectra, were used to evaluate the physical performance of both dynamical cores. In the implicit LES experiment, we confirmed that the high-order DGM with a polynomial order of \\(p=11\\) achieved a finer effective resolution than the FVM with third-order and seventh-order upwind schemes (UD3 and UD7). In contrast, in the explicit LES experiment, the effective resolution was largely determined by the subgrid-scale turbulence model, thereby reducing the relative advantage of high-order schemes. Our cost metrics, which combine the physical performance and computational resource usage, demonstrate that the DGM with \\(p=7,11\\) and the FVM with UD7 can achieve lower overall computational costs than the FVM with UD3 in both implicit and explicit LES experiments. Although the high-order DGM requires larger computational resources due to a stricter stability limit, its overall computational costs are reduced in the implicit LES experiment because of its finer effective resolution, as well as high computational efficiency associated with superior data locality and smaller inter-node communication overhead. On the other hand, to fully exploit the advantages of high-order schemes in explicit LES, it is necessary to redesign the turbulence model so that the filter length becomes consistent with the inherent effective resolution of the dynamical cores, and to relax the stricter stability limit for the DGM.

Recent studies have shown that spring land surface temperature (LST) and subsurface temperature (SUBT) over the high elevation areas in the western US (WUS) have significant impacts on the downstream summer droughts/floods in North America. In this paper, both the National Centers for Environmental Prediction—Global Forecast System (NCEP-GFS) general circulation model (GCM) and the weather research and forecasting (WRF) regional climate model (RCM) are employed, where RCM scenarios utilized initial and lateral boundary conditions derived from the corresponding NCEP-GFS scenarios. Here we use a late spring flood in the US Southern Great Plains (SGP) case to examine whether simulation of the LST/SUBT downstream effects is sensitive to the domain size choice, change in dynamical cores within the same model, as well as to the representation of surface processes parameterizations. Although all RCM experiments with different settings simulate reasonably geographical patterns of observed LST and precipitation anomalies, we found that the choice of the domain size is crucial for proper downscaling the LST/SUBT downstream effects to accurately produce the observed precipitation/LST anomalies over the SGP/WUS, respectively, along with the associated large-scale features. The southern boundary location has been identified to be crucial in producing the SGP Low Level Jet strength, which in turn brings more moisture from the Gulf of Mexico to the SGP and thereby resulting in a better simulation of the precipitation anomaly in that area. The sensitivity of the simulation of the LST/SUBT downstream effect to dynamical cores is assessed by inter-comparing the Non-hydrostatic Mesoscale Model (NMM) and the Advanced Research WRF dynamic cores. We find NMM was better at generating the large-scale eastward wave train, a crucial process associated with the LST/SUBT downstream effect. Meanwhile, this study also shows that the LST/SUBT downstream effects were not significantly dependent on the surface process parameterizations, although the Simplified Simple Biosphere model version 3 (SSiB3) highlighted a better performance over SSiB2.

Global numerical modeling is advancing into the era of kilometer‐scale, non‐hydrostatic simulations, while heterogeneous computing emerges as a pivotal trend in high‐performance computing (HPC). As a strong candidate for next‐generation global kilometer‐scale general circulation models, the A‐grid dynamical core based on the Low Mach number Approximate Riemann Solver must address key challenges: suppresses unphysical oscillations while preserving sharp gradients, mitigating Courant‐Friedrichs‐Lewy (CFL) constraints caused by vertically propagating sound waves, and making full use of heterogeneous computing power. This work presents LMARSpy, a GPU‐optimized non‐hydrostatic dry dynamical core with a sharpness‐preserving monotonicity limiter and a conservative vertical implicit solver. Designed for GPU efficiency, LMARSpy leverages a Python‐based HPC framework to ensure robust compatibility across heterogeneous computing environments. Benchmark tests validate the model's innovations: the limiter effectively suppresses unphysical oscillations while preserving sharpness, incurring only a 10.4% increase in GPU computational cost, as it is applied exclusively in the final sub‐step of the RK3 time‐stepping scheme; the Horizontally Explicit and Vertically Implicit scheme (employing a mass and potential temperature conservative vertical implicit solver) effectively mitigates vertical CFL limitations, delivering at least an order‐of‐magnitude efficiency improvement over explicit schemes when horizontal grid spacing substantially exceeds vertical spacing; and the Python‐based HPC framework enables seamless operation on both CPU and GPU architectures. When the computational scale is sufficient to fully utilize GPU memory, a single Nvidia RTX 3060 Ti GPU delivers 7.6 times the computational speed of a fully‐loaded 16‐thread Intel Core i5‐13490F CPU. Plain Language Summary As climate change intensifies, extreme weather events are becoming increasingly frequent and severe, necessitating high‐resolution numerical simulations to accurately capture sharp atmospheric changes and complex physical processes. A key challenge lies in resolving these sharp changes while ensuring numerical solution stability and preventing computational errors. Additionally, differences between vertical and horizontal grid resolutions impose strict numerical stability constraints, thereby reducing computational efficiency. Traditional CPU‐based weather models also struggle to adapt to the development of modern heterogeneous computing systems. To address these issues, we developed LMARSpy, a GPU‐optimized weather model featuring numerical limiters that preserve sharp gradients, vertical schemes that relax stability constraints, and a Python‐based high‐performance computing framework. LMARSpy can seamlessly integrate AI surrogate models, marking an important step toward efficient and accurate weather forecasting. Key Points The sharpness‐preserving monotonicity limiter suppresses unphysical oscillations while maintaining solution accuracy The conservative vertical implicit solver removes vertical Courant‐Friedrichs‐Lewy restrictions, enabling competitive computational acceleration The Python‐based high‐performance computing framework supporting GPU executions demonstrates desirable scalability

The scientific study of human consciousness has greatly benefited from the development of non-invasive brain imaging methods. The quest to identify the neural correlates of consciousness combined psychophysical experimentation with neuroimaging tools such as functional magnetic resonance imaging (fMRI) to map the changes in neural activity associated with conscious vs. unconscious percepts. Different neuroimaging methods have also been applied to characterize spontaneous brain activity fluctuations during altered states of consciousness, and to develop quantitative metrics for the level of consciousness. Most of these studies, however, have not explored the dynamic nature of the whole-brain imaging data provided by fMRI. A series of empirical and computational studies strongly suggests that the temporal fluctuations observed in this data present a non-trivial structure, and that this structure is compatible with the exploration of a discrete repertoire of states. In this review we focus on how dynamic neuroimaging can be used to address theoretical accounts of consciousness based on the hypothesis of a dynamic core, i.e. a constantly evolving and transiently stable set of coordinated neurons that constitute an integrated and differentiated physical substrate for each conscious experience. We review work exploring the possibility that metastability in brain dynamics leads to a repertoire of dynamic core states, and discuss how it might be modified during altered states of consciousness. This discussion prompts us to review neuroimaging studies aimed to map the dynamic exploration of the repertoire of states as a function of consciousness. Complementary studies of the dynamic core hypothesis using perturbative methods are also discussed. Finally, we propose that a link between metastability in brain dynamics and the level of consciousness could pave the way towards a mechanistic understanding of altered states of consciousness using tools from dynamical systems theory and statistical physics. •Contemporary theories of consciousness are introduced and discussed.•The relationship between these theories and brain metastability is discussed.•Dynamic connectivity studies addressing theoretical predictions are reviewed.•Perturbative methods to assess the repertoire of brain states are reviewed.

This study investigates the sensitivity of the boreal winter prediction skill of Community Atmosphere Model 5 to the choice of the dynamical core. Both finite volume (FV) and spectral element (SE) dynamical cores are tested. An additional FV with the SE topography (FV SE ) is also conducted to isolate the possible influence of the topography. The three dynamical core experiments, which ran from 2001/2002–2017/2018, are validated using Japanese 55 year reanalysis data. It turns out that the SE (−4.27 °C) has a smaller cold bias in boreal-winter surface air temperature (SAT) than the FV (−5.17 °C) and FV SE (−5.29 °C), particularly in North America, East Asia, and Southern Europe/Northern Africa. Significant North Atlantic Oscillation-like biases are also identified in the mid-troposphere. These biases affect seasonal prediction skills. Although the overall prediction skills of boreal-winter SAT, quantified by the anomaly correlation coefficient (ACC), and root-mean-square error (RMSE), are reasonably good (ACC = 0.40 and RMSE = 0.47 in the mean values of SE, FV, and FV SE ), they significantly differ from one region to another, depending on the choice of dynamical cores. For North America and Southern Europe/Northern Africa, SE shows better skills than FV SE and FV. Conversely, in East Asia, FV and FV SE outperform SE. These results suggest that the appropriate choice of the dynamical cores and the bottom boundary conditions could improve the boreal-winter seasonal prediction on a regional scale.

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.