It is the purpose of this paper to provide a comprehensive documentation of the new NCAR (National Center for Atmospheric Research) version of the spectral element (SE) dynamical core as part of the Community Earth System Model (CESM2.0) release. This version differs from previous releases of the SE dynamical core in several ways. Most notably the hybrid sigma vertical coordinate is based on dry air mass, the condensates are dynamically active in the thermodynamic and momentum equations (also referred to as condensate loading), and the continuous equations of motion conserve a more comprehensive total energy that includes condensates. Not related to the vertical coordinate change, the hyperviscosity operators and the vertical remapping algorithms have been modified. The code base has been significantly reduced, sped up, and cleaned up as part of integrating SE as a dynamical core in the CAM (Community Atmosphere Model) repository rather than importing the SE dynamical core from High‐Order Methods Modeling environment as an external code.

A long-term study of coherent turbulence structures in the atmospheric surface layer has been carried out using 10 months of turbulence data taken on a 30-m tower under varying meteorological conditions. We use an objective detection technique based on wavelet transforms. The applied technique permits the isolation of the coherent structures from small-scale background fluctuations which is necessary for the development of dynamical models describing the evolution and properties of these phenomena. It was observed that coherent structures occupied 36% of the total time with mean turbulent flux contributions of 44% for momentum and 48% for heat. The calculation of a transport efficiency parameter indicates that coherent structures transport heat more efficiently than momentum. Furthermore, the transport efficiency increases with increasing contribution of the structures to the overall transport

Highlights• A new Global Climate Model for Saturn with radiative transfer • High-resolution numerical simulations on a duration of 15 Saturn years • Results on zonal jets, waves, eddies in Saturn's troposphere AbstractThe Cassini mission unveiled the intense and diverse activity in Saturn's atmosphere: banded jets, waves, vortices, equatorial oscillations. To set the path towards a better understanding of those phenomena, we performed high-resolution multi-annual numerical simulations of Saturn's atmospheric dynamics. We built a new Global Climate Model [GCM] for Saturn, named the Saturn DYNAMICO GCM, by combining a radiative-seasonal model tailored for Saturn to a hydrodynamical solver based on an icosahedral grid suitable for massively-parallel architectures. The impact of numerical dissipation, and the conservation of angular momentum, are examined in the model before a reference simulation employing the Saturn DYNAMICO GCM with a 1/2 • latitude-longitude resolution is considered for analysis. Mid-latitude banded jets showing similarity with observations are reproduced by our model. Those jets are accelerated and maintained by eddy momentum transfers to the mean flow, with the magnitude of momentum fluxes compliant with the observed values. The eddy activity is not regularly distributed with time, but appears as bursts; both barotropic and baroclinic instabilities could play a role in the eddy activity. The steady-state latitude of occurrence of jets is controlled by poleward migration during the spin-up of our model. At the equator, a weaklysuperrotating tropospheric jet and vertically-stacked alternating stratospheric jets are obtained in our GCM simulations. The model produces Yanai (Rossby-gravity), Rossby and Kelvin waves at the equator, as well as extratropical Rossby waves, and large-scale vortices in polar regions. Challenges remain to reproduce Saturn's powerful superrotating jet and hexagon-shaped circumpolar jet in the troposphere, and downward-propagating equatorial oscillation in the stratosphere.

Context. The anomalously large radii of hot Jupiters has long been a mystery. However, by combining both theoretical arguments and 2D models, a recent study has suggested that the vertical advection of potential temperature leads to a hotter adiabatic temperature profile in the deep atmosphere than the profile obtained with standard 1D models. Aims. In order to confirm the viability of that scenario, we extend this investigation to 3D, time-dependent models. Methods. We use a 3D general circulation model DYNAMICO to perform a series of calculations designed to explore the formation and structure of the driving atmospheric circulations, and detail how it responds to changes in both the upper and deep atmospheric forcing.Results. In agreement with the previous, 2D study, we find that a hot adiabat is the natural outcome of the long-term evolution of the deep atmosphere. Integration times of the order of 1500 yr are needed for that adiabat to emerge from an isothermal atmosphere, explaining why it has not been found in previous hot Jupiter studies. Models initialised from a hotter deep atmosphere tend to evolve faster toward the same final state. We also find that the deep adiabat is stable against low-levels of deep heating and cooling, as long as the Newtonian cooling timescale is longer than ∼3000 yr at 200 bar. Conclusions. We conclude that steady-state vertical advection of potential temperature by deep atmospheric circulations constitutes a robust mechanism to explain the inflated radii of hot Jupiters. We suggest that future models of hot Jupiters be evolved for a longer time than currently done, and when possible that models initialised with a hot deep adiabat be included. We stress that this mechanism stems from the advection of entropy by irradiation-induced mass flows and does not require a (finely tuned) dissipative process, in contrast with most previously suggested scenarios.

Abstract.A new algorithm is presented for the solution of the shallow water equations on quasi-uniform spherical grids. It combines a mimetic finite volume spatial discretization with a Crank-Nicolson time discretization of fast waves and an accurate and conservative forward-in-time advection scheme for mass and potential vorticity (PV). The algorithm is implemented and tested on two families of grids: hexagonal-icosahedral Voronoi grids, and modified equiangular cubed-sphere grids.Results of a variety of tests are presented, including convergence of the discrete scalar Laplacian and Coriolis operators, advection, solid body rotation, flow over an isolated mountain, and a barotropically unstable jet. The results confirm a number of desirable properties for which the scheme was designed: exact mass conservation, very good available energy and potential enstrophy conservation, consistent mass, PV and tracer transport, and good preservation of balance including vanishing ∇ × ∇, steady geostrophic modes, and accurate PV advection. The scheme is stable for large wave Courant numbers and advective Courant numbers up to about 1.In the most idealized tests the overall accuracy of the scheme appears to be limited by the accuracy of the Coriolis and other mimetic spatial operators, particularly on the cubed-sphere grid. On the hexagonal grid there is no evidence for damaging effects of computational Rossby modes, despite attempts to force them explicitly.

Abstract. The design of the icosahedral dynamical core DY-NAMICO is presented. DYNAMICO solves the multi-layer rotating shallow-water equations, a compressible variant of the same equivalent to a discretization of the hydrostatic primitive equations in a Lagrangian vertical coordinate, and the primitive equations in a hybrid mass-based vertical coordinate. The common Hamiltonian structure of these sets of equations is exploited to formulate energy-conserving spatial discretizations in a unified way.The horizontal mesh is a quasi-uniform icosahedral C-grid obtained by subdivision of a regular icosahedron. Control volumes for mass, tracers and entropy/potential temperature are the hexagonal cells of the Voronoi mesh to avoid the fast numerical modes of the triangular C-grid. The horizontal discretization is that of Ringler et al. (2010), whose discrete quasi-Hamiltonian structure is identified. The prognostic variables are arranged vertically on a Lorenz grid with all thermodynamical variables collocated with mass. The vertical discretization is obtained from the three-dimensional Hamiltonian formulation. Tracers are transported using a second-order finite-volume scheme with slope limiting for positivity. Explicit Runge-Kutta time integration is used for dynamics, and forward-in-time integration with horizontal/vertical splitting is used for tracers. Most of the model code is common to the three sets of equations solved, making it easier to develop and validate each piece of the model separately.Representative three-dimensional test cases are run and analyzed, showing correctness of the model. The design permits to consider several extensions in the near future, from higher-order transport to more general dynamics, especially deep-atmosphere and non-hydrostatic equations.

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 NavierStokes 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.

We introduce an innovative wavelet-based approach to dynamically adjust the local grid resolution to maintain a uniform specified error tolerance. Extending the work of [4], a wavelet multi-scale approximation is used to make dynamically adaptive the TRiSK model [13] for the rotating shallow water equations on the sphere. This paper focuses on the challenges encountered when extending the adaptive wavelet method to the sphere and ensuring an efficient parallel implementation using mpi. The wavelet method is implemented in fortran95 with an emphasis on computational efficiency and scales well up to O(10 2 ) processors for load-unbalanced scenarios and up to at least O(10 3 ) processors for load-balanced scenarios. The method is verified using standard smooth test cases [22] and a nonlinear test case proposed by [5]. The dynamical grid adaption provides compression ratios of up to 50 times in a challenging homogenous turbulence test case. The adaptive code is about three times slower per active grid point than the equivalent non-adaptive TRiSK code and about four times slower per active grid point than an equivalent spectral code. This computationally efficient adaptive dynamical core could serve as the foundation on which to build a complete climate or weather model.