Symmetry group of the equiangular cubed sphere

The equiangular cubed sphere is a spherical grid, widely used in computational physics. This paper deals with mathematical properties of this grid. We identify the symmetry group, i.e. the group of the orthogonal transformations that leave the cubed sphere invariant. The main result is that it coincides with the symmetry group of a cube. The proposed proof emphasizes metric properties of the cubed sphere. We study the geodesic distance on the grid, which reveals that the shortest geodesic arcs match with the vertices of a cuboctahedron. The results of this paper lay the foundation for future numerical schemes, based on rotational invariance of the cubed sphere.

Grid-stretching capability for the GEOS-Chem 13.0.0 atmospheric chemistry model

Modeling atmospheric chemistry at fine resolution globally is computationally expensive; the capability to focus on specific geographic regions using a multiscale grid is desirable. Here, we develop, validate, and demonstrate stretched grids in the GEOS-Chem atmospheric chemistry model in its high-performance implementation (GCHP). These multiscale grids are specified at runtime by four parameters that offer users nimble control of the region that is refined and the resolution of the refinement. We validate the stretched-grid simulation versus global cubed-sphere simulations. We demonstrate the operation and flexibility of stretched-grid simulations with two case studies that compare simulated tropospheric NO2 column densities from stretched-grid and cubed-sphere simulations to retrieved column densities from the TROPOspheric Monitoring Instrument (TROPOMI). The first case study uses a stretched grid with a broad refinement covering the contiguous US to produce simulated columns that perform similarly to a C180 (∼ 50 km) cubed-sphere simulation at less than one-ninth the computational expense. The second case study experiments with a large stretch factor for a global stretched-grid simulation with a highly localized refinement with ∼10 km resolution for California. We find that the refinement improves spatial agreement with TROPOMI columns compared to a C90 cubed-sphere simulation of comparable computational demands. Overall, we find that stretched grids in GEOS-Chem are a practical tool for fine-resolution regional- or continental-scale simulations of atmospheric chemistry. Stretched grids are available in GEOS-Chem version 13.0.0.

A Positivity-preserving Conservative Semi-Lagrangian Multi-moment Global Transport Model on the Cubed Sphere

A positivity-preserving conservative semi-Lagrangian transport model by multi-moment finite volume method has been developed on the cubed-sphere grid. Two kinds of moments (i.e., point values (PV moment) at cell interfaces and volume integrated average (VIA moment) value) are defined within a single cell. The PV moment is updated by a conventional semi-Lagrangian method, while the VIA moment is cast by the flux form formulation to assure the exact numerical conservation. Different from the spatial approximation used in the CSL2 (conservative semi-Lagrangian scheme with second order polynomial function) scheme, a monotonic rational function which can effectively remove non-physical oscillations is reconstructed within a single cell by the PV moments and VIA moment. To achieve exactly positive-definite preserving, two kinds of corrections are made on the original conservative semi-Lagrangian with rational function (CSLR) scheme. The resulting scheme is inherently conservative, non-negative, and allows a Courant number larger than one. Moreover, the spatial reconstruction can be performed within a single cell, which is very efficient and economical for practical implementation. In addition, a dimension-splitting approach coupled with multi-moment finite volume scheme is adopted on cubed-sphere geometry, which benefitsthe implementation of the 1D CSLR solver with large Courant number. The proposed model is evaluated by several widely used benchmark tests on cubed-sphere geometry. Numerical results show that the proposed transport model can effectively remove nonphysical oscillations and preserve the numerical non-negativity, and it has the potential to transport the tracers accurately in a real atmospheric model.

fv3gfs-wrapper: a Python wrapper of the FV3GFS atmospheric model

Simulation software in geophysics is traditionally written in Fortran or C++ due to the stringent performance requirements these codes have to satisfy. As a result, researchers who use high-productivity languages for exploratory work often find these codes hard to understand, hard to modify, and hard to integrate with their analysis tools. fv3gfs-wrapper is an open-source Python-wrapped version of the NOAA (National Oceanic and Atmospheric Administration) FV3GFS (Finite-Volume Cubed-Sphere Global Forecast System) global atmospheric model, which is coded in Fortran. The wrapper provides simple interfaces to progress the Fortran main loop and get or set variables used by the Fortran model. These interfaces enable a wide range of use cases such as modifying the behavior of the model, introducing online analysis code, or saving model variables and reading forcings directly to and from cloud storage. Model performance is identical to the fully compiled Fortran model, unless routines to copy the state in and out of the model are used. This copy overhead is well within an acceptable range of performance and could be avoided with modifications to the Fortran source code. The wrapping approach is outlined and can be applied similarly in other Fortran models to enable more productive scientific workflows.

On the sensitivity of hurricane intensity and structure to horizontal tracer advection schemes in FV3

We investigate the sensitivity of hurricane intensity and structure to the horizontal tracer advection in the Geophysical Fluid Dynamics Laboratory (GFDL) Finite-Volume Cubed-Sphere Dynamical Core (FV3). We compare two schemes, a monotonic scheme and a less diffusive positive-definite scheme. The positive-definite scheme leads to significant improvement in the intensity prediction relative to the monotonic scheme in a suite of five-day forecasts that mostly consist of rapidly intensifying hurricanes. Notable storm structural differences are present: the radius of maximum wind (RMW) is smaller and eyewall convection occurs farther inside the RMW when the positive-definite scheme is used. Moreover, we find that the horizontal tracer advection scheme affects the eyewall convection location by affecting the moisture distribution in the inner-core region. This study highlights the importance of dynamical core algorithms in hurricane intensity prediction.

Structure and Dynamics of Ensemble Correlations for Satellite All-Sky Observations in an FV3-Based Global-to-Regional Nested Convection-Permitting Ensemble Forecast of Hurricane Harvey

There are ongoing efforts to establish an ensemble data assimilation and prediction system for tropical cyclones based on the FV3 (finite-volume cubed-sphere) dynamic core with the capability to assimilate satellite all-sky infrared and microwave observations. To complement the system developments and improve our understanding of the assimilation of all-sky infrared and microwave observations, this study assesses their potential impacts on the analysis of Hurricane Harvey (2017) through examinations of the structure and dynamics of the ensemble-based correlations as well as single observation data assimilation experiments, using an ensemble forecast generated by a global-to-regional nested FV3-based model. It is found that different infrared and microwave channels are sensitive to different types of hydrometeors within different layers of the atmosphere, and the correlations vanish beyond 200 km in the region covered by cloud or abundant hydrometeors. The spatial correlations between brightness temperatures and model states will adjust the structure and intensity of the hurricane in the model so that the simulated hurricane will better fit the “observed” brightness temperatures. In general, these results show how assimilating infrared and microwave together can improve the analyses of tropical cyclone intensity and structure, which may lead to improved intensity forecasts.

Interpolating data on the Cubed Sphere with Spherical Harmonics

<p>The Cubed Sphere is a grid commonly used in numerical simulation in climatology. In this talk we present recent progress<br>on the algebraic and geometrical properties of this highly symmetrical grid.<br>First, an analysis of the symmetry group of the Cubed Sphere will be presented: this group <br>is identified as the group of the Cube, [1]. Furthermore, we show how to construct a discrete Spherical Harmonics (SH) basis associated to <br>the Cubed Sphere. This basis displays a truncation scheme relating the zonal and longitudinal <br>mode numbers reminiscent of the rhomboidal truncation on the Lon-Lat grid.<br>The new analysis allows to derive new quadrature rules of  interest for applications in any kind of spherical modelling. In addition,<br>we will comment on applications in mathematical climatology and meteorology, [2].</p><p>[1] J.-B. Bellet, Symmetry group of the equiangular Cubed Sphere, preprint, IECL, Univ. Lorraine, 2020, submitted</p><p>[2] J.-B. Bellet, M. Brachet and J.-P. Croisille, Spherical Harmonics on The Cubed Sphere, IECL, Univ. Lorraine, 2021, Preprint.</p>