A semi-implicit compressible model for atmospheric flows with seamless access to soundproof and hydrostatic dynamics

We introduce a second-order numerical scheme for compressible atmospheric motions at small to planetary scales. The collocated finite volume method treats the advection of mass, momentum, and mass-weighted potential temperature in conservation form while relying on Exner pressure for the pressure gradient term. It discretises the rotating compressible equations by evolving full variables rather than perturbations around a background state, and operates with time steps constrained by the advection speed only. Perturbation variables are only used as auxiliary quantities in the formulation of the elliptic problem. Borrowing ideas on forward-in-time differencing, the algorithm reframes the authors' previously proposed schemes into a sequence of implicit midpoint, advection, and implicit trapezoidal steps that allows for a time integration unconstrained by the internal gravity wave speed. Compared with existing approaches, results on a range of benchmarks of nonhydrostatic- and hydrostatic-scale dynamics are competitive. The test suite includes a new planetary-scale inertia-gravity wave test highlighting the properties of the scheme and its large time step capabilities. In the hydrostatic-scale cases the model is run in pseudo-incompressible and hydrostatic mode with simple switching within a uniform discretization framework. The differences with the compressible runs return expected relative magnitudes. By providing seamless access to soundproof and hydrostatic dynamics, the developments represent a necessary step towards an all-scale blended multimodel solver

A mixed finite-element, finite-volume, semi-implicit discretisation for atmospheric dynamics: Cartesian geometry

This is the author accepted manuscript. The final version is available from Wiley via the DOI in this recordTo meet the challenges posed by future generations of massively parallel supercomputers a reformulation of the dynamical core for the Met Office’s weather and climate model is presented. This new dynamical core uses explicit finite-volume type discretisations for the transport of scalar fields coupled with an iterated-implicit, mixed finite-element discretisation for all other terms. The target model aims to maintain the accuracy, stability and mimetic properties of the existing Met Office model independent of the chosen mesh while improving the conservation properties of the model. This paper details that proposed formulation and, as a first step towards complete testing, demonstrates its performance for a number of test cases in (the context of) a Cartesian domain. The new model is shown to produce similar results to both the existing semi-implicit semi-Lagrangian model used at the Met Office and other models in the literature on a range of bubble tests and orographically forced flows in two and three dimensions.Natural Environment Research Council (NERC

Effects of Initial Flow on Close-In Planet Atmospheric Circulation

We use a general circulation model to study the three-dimensional (3-D) flow and temperature distributions of atmospheres on tidally synchronized extrasolar planets. In this work, we focus on the sensitivity of the evolution to the initial flow state, which has not received much attention in 3-D modeling studies. We find that different initial states lead to markedly different distributions-even under the application of strong forcing (large day-night temperature difference with a short "thermal drag time") that may be representative of close-in planets. This is in contrast with the results or assumptions of many published studies. In general, coherent jets and vortices (and their associated temperature distributions) characterize the flow, and they evolve differently in time, depending on the initial condition. If the coherent structures reach a quasi- stationary state, their spatial locations still vary. The result underlines the fact that circulation models are currently unsuitable for making quantitative predictions (e.g., location and size of a "hot spot") without better constrained, and well posed, initial conditions.Comment: Accepted for publication in the Astrophysical Journal; 23 pages, 9 figures

A mountain-induced moist baroclinic wave test case for the dynamical cores of atmospheric general circulation models

Idealized test cases for the dynamical cores of atmospheric general circulation models are informative tools to assess the accuracy of the numerical designs and investigate the general characteristics of atmospheric motions. A new test case is introduced that is built upon a baroclinically unstable base state with an added orographic barrier. The topography is analytically prescribed and acts as a trigger of both baroclinic Rossby waves and inertia–gravity waves on a rotating, regular-sized planet. Both dry and idealized moist configurations are suggested. The latter utilizes the Kessler warm-rain precipitation scheme. The test case enhances the complexity of the existing test suite hierarchy and focuses on the impacts of two midlatitudinal mountain ridges on the circulation. Selected simulation examples from four dynamical cores are shown. These are the Spectral Element and Finite Volume dynamical cores, which are part of the National Center for Atmospheric Research (NCAR) Community Earth System Model (CESM), versions 2.1.3 and 2.2, and the Cubed-Sphere Finite Volume dynamical cores, which is new to CESM version 2.2. In addition, the Model for Prediction Across Scales (MPAS) is tested. The overall flow patterns agree well in the four dynamical cores, but the details can vary greatly. The examples highlight the broad palette of use cases for the test case and reveal physics–dynamics coupling issues.</p