We investigate mechanisms governing moist energy exchanges at the atmosphere-ocean interface in global Earth system models. The goal of this work is to overcome deficiencies like energy fixers and unphysical thermodynamic formulations and designs that are commonly used in modern models. For example, while the ocean surface evaporation is one of the most significant climatological drivers, its representation in numerical models may not be physically accurate. In particular, existing schemes give an incorrect atmospheric air temperature tendency during evaporation events. To remedy this, starting from first principles, we develop a new mechanism for the ocean-atmosphere moist energy transfers. It utilizes consistent thermodynamics of water species, distributes latent heat of evaporation in a physically plausible way, and avoids reliance on artificial energy fixers. The temperature and water mass tendencies are used to formulate a set of ordinary differential equations (ODEs) representing a simple box model of ocean-air exchange. We investigate the properties of the ODEs representing the proposed mechanism and compare them against those derived from the current designs of the Energy Exascale Earth System Model (E3SM). The proposed simplified box model highlights the advantages of our approach in capturing physically appropriate atmospheric temperature changes during evaporation while conserving energy.

Much attention has recently been devoted to data-based computing of evolution of physical systems. In such approaches, information about data points from past trajectories in phase space is used to reconstruct the equations of motion and to predict future solutions that have not been observed before. However, in many cases, the available data does not correspond to the variables that define the system's phase space. We focus our attention on the important example of dissipative dynamical systems. In that case, the phase space consists of coordinates, momenta and entropies; however, the momenta and entropies cannot, in general, be observed directly. To address this difficulty, we develop an efficient data-based computing framework based exclusively on observable variables, by constructing a novel approach based on the thermodynamic Lagrangian, and constructing neural networks that respect the thermodynamics and guarantees the non-decreasing entropy evolution. We show that our network can provide an efficient description of phase space evolution based on a limited number of data points and a relatively small number of parameters in the system.

To accurately compute data-based prediction of Hamiltonian systems, it is essential to utilize methods that preserve the structure of the equations over time. We consider a particularly challenging case of systems with interacting parts that do not reduce to pure momentum evolution. Such systems are essential in scientific computations, such as discretization of a continuum elastic rod, which can be viewed as the group of rotations and translations SE(3). The evolution involves not only the momenta but also the relative positions and orientations of the particles. The presence of Lie group-valued elements, such as relative positions and orientations, poses a problem for applying previously derived methods for data-based computing. We develop a novel method of data-based computation and complete phase space learning of such systems. We follow the original framework of SympNets (Jin et al., 2020) and LPNets (Eldred et al., 2024), building the neural network from phase space mappings that preserve the Lie-Poisson structure. We derive a novel system of mappings that are built into neural networks describing the evolution of such systems. We call such networks Coupled Lie-Poisson Neural Networks, or CLPNets. We consider increasingly complex examples for the applications of CLPNets, starting with the rotation of two rigid bodies about a common axis, progressing to the free rotation of two rigid bodies, and finally to the evolution of two connected and interacting SE(3) components, describing the discretization of an elastic rod into two elements. Our method preserves all Casimir invariants to machine precision, preserves energy to high accuracy, and shows good resistance to the curse of dimensionality, requiring only a few thousand data points for all cases studied (three to eighteen dimensions). Additionally, the method is highly economical in memory requirements, requiring only about 200 parameters for the most complex case considered.

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.

An accurate data-based prediction of the long-term evolution of Hamiltonian systems requires a network that preserves the appropriate structure under each time step. Every Hamiltonian system contains two essential ingredients: the Poisson bracket and the Hamiltonian. Hamiltonian systems with symmetries, whose paradigm examples are the Lie-Poisson systems, have been shown to describe a broad category of physical phenomena, from satellite motion to underwater vehicles, fluids, geophysical applications, complex fluids, and plasma physics. The Poisson bracket in these systems comes from the symmetries, while the Hamiltonian comes from the underlying physics. We view the symmetry of the system as primary, hence the Lie-Poisson bracket is known exactly, whereas the Hamiltonian is regarded as coming from physics and is considered not known, or known approximately. Using this approach, we develop a network based on transformations that exactly preserve the Poisson bracket and the special functions of the Lie-Poisson systems (Casimirs) to machine precision. We present two flavors of such systems: one, where the parameters of transformations are computed from data using a dense neural network (LPNets), and another, where the composition of transformations is used as building blocks (G-LPNets). We also show how to adapt these methods to a larger class of Poisson brackets. We apply the resulting methods to several examples, such as rigid body (satellite) motion, underwater vehicles, a particle in a magnetic field, and others. The methods developed in this paper are important for the construction of accurate data-based methods for simulating the long-term dynamics of physical systems.

Motivated by modelling and numerical applications in geophysical fluid dynamics, such as the outflow of free or forced waves, we present a Lagrangian variational formulation for fluids exchanging energy with its surrounding through the boundary of its spatial domain. We give the variational formulation in the material description and deduce the Eulerian variational formulation by applying reduction by symmetry in the Lagrangian framework. In the material description we use the classical Hamilton principle applied to fluid trajectories, appropriately amended to incorporate boundary forces via a Lagrange-d’Alembert approach, and to take into account only the fluid particles present in the fluid domain. In particular, our approach extends to the case of permeable domains the well-known geometric description of fluid motion via diffeomorphism groups.

Abstract We develop a doubly periodic version of the Simple Convection‐Permitting E3SM Atmosphere Model (SCREAM) to provide an efficient configuration for this global convection permitting model (GCPM), akin to a single column model often found in conventional general circulation models. The design details are explained, in addition to the extensive case library associated with the doubly periodic SCREAM (DP‐SCREAM) configuration. We demonstrate that doubly periodic cloud resolving models are useful tools to explore the horizontal resolution sensitivity of GCPMs, in addition to replicating biases seen in the global models. Using DP‐SCREAM, we show that SCREAM exhibits behaviors of a scale aware model as it is able to naturally partition between sub‐grid scale (SGS) and resolved vertical transport across the gray zone of turbulence. We show that SCREAM is reasonably scale insensitive when run at resolutions from 1 to 5 km, but can exhibit sensitivity, particularly for the shallow convective regime, when run at resolutions approaching that of large eddy simulations. We conclude that SGS parameterization improvements are likely needed to reduce this scale sensitivity.

Abstract This study investigates inherent numerical dissipation due to upwind fluxes and reconstruction strategies for collocated Finite‐Volume integration of the Euler equations. Idealized supercell simulations are used without any explicit dissipation. Flux terms are split into: mass flux, pressure, and advected quantities. They are computed with the following upwind strategies: central, advectively upwind, and acoustically upwind. This is performed for third and ninth‐order‐accurate reconstructions with and without Weighted Essentially Non‐Oscillatory limiting. Acoustic‐only upwinding for pressure and mass flux terms and advective‐only upwinding for advected quantities is the most flexible simplification found. It reduces data movement and computations. Assuming a constant speed of sound in acoustic upwinding gives similar results to using the true speed of sound. Dissipation from upwind adapts automatically to grid spacing, time step, reconstruction accuracy, and flow smoothness. While stability is maintained even at 21st‐order spatial accuracy, there is a limit to the spatial order of accuracy for which upwinding alone can create a realizable solution in the conditions of this study. Convex combinations of upwind and central solutions for flux terms also reduced dissipation, but as the central proportion grows, solutions become physically unrealizable. The range of length scales of the kinetic energy spectra can be extended along k−5/3 to smaller spatial scales by reducing dissipation either with higher‐order reconstructions or using convex combinations of upwind and central fluxes. However, not all extensions of the length scale range along k−5/3 exhibit physically realizable solutions, even though the spectra appear to be physical.

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Fourier analyses of continuous and discontinuous Galerkin methods of arbitrary degree of approximation Daniel Le Roux, Christopher Eldred, Mark Taylor

Earth and Space Science Open Archive This work has been accepted for publication in Journal of Advances in Modeling Earth Systems (JAMES). Version of RecordESSOAr is a venue for early communication or feedback before peer review. Data may be preliminary. Learn more about preprints. preprintOpen AccessYou are viewing an older version [v1]Go to new versionConvection-Permitting Simulations with the E3SM Global Atmosphere ModelAuthorsPeter MartinCaldwelliDChristopher RyutaroTeraiiDBenjamin RHillmanNoel D.KeeniDPeter ABogenschutzWuyinLinHassanBeydouniDMark ATayloriDLucaBertagnaiDAndrewBradleyThomas CClevengeriDAaron SheffieldDonahueiDChrisEldredJames GFoucarJean-ChristopheGolaziDOksanaGubaRobert LJacobJeffJohnsoniDJagadishKrishnaWeiranLiuiDKyle GPresselAndrew G.SalingeriDBalwinderSinghAndrewSteyerPaulUllrichiDDanqingWuXingqiuYuanJacobShpundHsi-YenMaiDCharles SuttonZenderiDSee all authors Peter Martin CaldwelliDCorresponding Author• Submitting AuthorLawrence Livermore National Laboratory (DOE)iDhttps://orcid.org/0000-0001-8604-0844view email addressThe email was not providedcopy email addressChristopher Ryutaro TeraiiDUniversity of California - IrvineiDhttps://orcid.org/0000-0002-2433-0472view email addressThe email was not providedcopy email addressBenjamin R HillmanSandia National Laboratoriesview email addressThe email was not providedcopy email addressNoel D. KeeniDLawrence Berkeley National Laboratory (DOE)iDhttps://orcid.org/0000-0003-3607-3554view email addressThe email was not providedcopy email addressPeter A BogenschutzLawrence Livermore National Laboratoryview email addressThe email was not providedcopy email addressWuyin LinBrookhaven National Laboratoryview email addressThe email was not providedcopy email addressHassan BeydouniDKarlsruhe Institute of TechnologyiDhttps://orcid.org/0000-0003-4094-8173view email addressThe email was not providedcopy email addressMark A TayloriDSandia National LaboratoriesiDhttps://orcid.org/0000-0002-9267-2554view email addressThe email was not providedcopy email addressLuca BertagnaiDUnknowniDhttps://orcid.org/0000-0002-6171-3202view email addressThe email was not providedcopy email addressAndrew BradleySandia National Laboratoryview email addressThe email was not providedcopy email addressThomas C ClevengeriDSandia National LabiDhttps://orcid.org/0000-0002-3340-2482view email addressThe email was not providedcopy email addressAaron Sheffield DonahueiDLawrence Livermore National LaboratoryiDhttps://orcid.org/0000-0002-4710-753Xview email addressThe email was not providedcopy email addressChris EldredLAGA, University of Parisview email addressThe email was not providedcopy email addressJames G FoucarSandia National Laboratory (DOE)view email addressThe email was not providedcopy email addressJean-Christophe GolaziDLawrence Livermore National Laboratory (DOE)iDhttps://orcid.org/0000-0003-1616-5435view email addressThe email was not providedcopy email addressOksana GubaSandia National Laboratoriesview email addressThe email was not providedcopy email addressRobert L JacobArgonne Notional Laboratoryview email addressThe email was not providedcopy email addressJeff JohnsoniDCohere LLCiDhttps://orcid.org/0000-0002-0265-5241view email addressThe email was not providedcopy email addressJagadish KrishnaUnknownview email addressThe email was not providedcopy email addressWeiran LiuiDUC DavisiDhttps://orcid.org/0000-0002-7559-4726view email addressThe email was not providedcopy email addressKyle G PresselPacific Northwest National Laboratoryview email addressThe email was not providedcopy email addressAndrew G. SalingeriDSandia National LaboratoryiDhttps://orcid.org/0000-0003-4692-6813view email addressThe email was not providedcopy email addressBalwinder SinghPacific Northwest National Laboratory (DOE)view email addressThe email was not providedcopy email addressAndrew SteyerSandia National Laboratoryview email addressThe email was not providedcopy email addressPaul UllrichiDUniversity of California DavisiDhttps://orcid.org/0000-0003-4118-4590view email addressThe email was not providedcopy email addressDanqing WuArgonne National Labview email addressThe email was not providedcopy email addressXingqiu YuanArgonne National Labview email addressThe email was not providedcopy email addressJacob ShpundUnknownview email addressThe email was not providedcopy email addressHsi-Yen MaiDLLNLiDhttps://orcid.org/0000-0002-9628-1278view email addressThe email was not providedcopy email addressCharles Sutton ZenderiDUniversity of California, IrvineiDhttps://orcid.org/0000-0003-0129-8024view email addressThe email was not providedcopy email address

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.

The time integration scheme is probably one of the most fundamental choices in the development of an ocean model. In this paper, we investigate several time integration schemes when applied to the shallow water equations. This set of equations is accurate enough for the modeling of a shallow ocean and is also relevant to study as it is the one solved for the barotropic (i.e. vertically averaged) component of a three dimensional ocean model. We analyze different time stepping algorithms for the linearized shallow water equations. High order explicit schemes are accurate but the time step is constrained by the Courant-Friedrichs-Lewy stability condition. Implicit schemes can be unconditionally stable but, in practice lack accuracy when used with large time steps. In this paper we propose a detailed comparison of such classical schemes with exponential integrators. The accuracy and the computational costs are analyzed in different configurations.