Cubed-sphere Grid Research Articles

A high-order conservative collocation scheme and its application to global shallow-water equations

Abstract. In this paper, an efficient and conservative collocation method is proposed and used to develop a global shallow-water model. Being a nodal type high-order scheme, the present method solves the pointwise values of dependent variables as the unknowns within each control volume. The solution points are arranged as Gauss–Legendre points to achieve high-order accuracy. The time evolution equations to update the unknowns are derived under the flux reconstruction (FR) framework (Huynh, 2007). Constraint conditions used to build the spatial reconstruction for the flux function include the pointwise values of flux function at the solution points, which are computed directly from the dependent variables, as well as the numerical fluxes at the boundaries of the computational element, which are obtained as Riemann solutions between the adjacent elements. Given the reconstructed flux function, the time tendencies of the unknowns can be obtained directly from the governing equations of differential form. The resulting schemes have super convergence and rigorous numerical conservativeness. A three-point scheme of fifth-order accuracy is presented and analyzed in this paper. The proposed scheme is adopted to develop the global shallow-water model on the cubed-sphere grid, where the local high-order reconstruction is very beneficial for the data communications between adjacent patches. We have used the standard benchmark tests to verify the numerical model, which reveals its great potential as a candidate formulation for developing high-performance general circulation models.

Hermitian approximation of the spherical divergence on the Cubed-Sphere

Previous work (Croisille, 2013) showed that the Cubed-Sphere grid offers a suitable discrete framework for extending Hermitian compact operators (Collatz, 1960) to the spherical setup. In this paper we further investigate the design of high-order accurate approximations of spherical differential operators on the Cubed-Sphere with an emphasis on the spherical divergence of a tangent vector field. The basic principle of this approximation relies on evaluating pointwise Hermitian derivatives along a series of great circles covering the sphere. Several test-cases demonstrate the very good accuracy of the approximate spherical divergence calculated with the new scheme.

Representer-based variational data assimilation in a spectral element shallow water model on the cubed-sphere grid

A representer-based variational data assimilation system is newly developed for the spectral element shallow water model in the High Order Method Modeling Environment. This study includes the development of tangent linear and adjoint codes and a background error covariance model. The correctness of the developed codes were checked by various ways such as linearity tests for tangent linear codes, adjoint tests for adjoint codes and symmetric tests for representer functions, which are four-dimensional covariance functions in observation-space. Then, direct and indirect representer-based data assimilation systems were constructed and evaluated by performing a series of identical twin experiments, where synthetic data were obtained from a reference run (nature run) and assimilated to correct initial conditions. The characteristics of the covariance model according to the different horizontal scales were evaluated by a suite of single-observation experiments. The results show satisfactory behaviours for both direct and indirect representer-based variational data assimilation methods, which indicates that they are ready to be further developed as a full-fledged four-dimensional variational data assimilation system as next step.

High-order central ENO finite-volume scheme for hyperbolic conservation laws on three-dimensional cubed-sphere grids

A fourth-order accurate finite-volume scheme for hyperbolic conservation laws on three-dimensional (3D) cubed-sphere grids is described. The approach is based on a central essentially non-oscillatory (CENO) finite-volume method that was recently introduced for two-dimensional compressible flows and is extended to 3D geometries with structured hexahedral grids. Cubed-sphere grids feature hexahedral cells with nonplanar cell surfaces, which are handled with high-order accuracy using trilinear geometry representations in the proposed approach. Varying stencil sizes and slope discontinuities in grid lines occur at the boundaries and corners of the six sectors of the cubed-sphere grid where the grid topology is unstructured, and these difficulties are handled naturally with high-order accuracy by the multidimensional least-squares based 3D CENO reconstruction with overdetermined stencils. A rotation-based mechanism is introduced to automatically select appropriate smaller stencils at degenerate block boundaries, where fewer ghost cells are available and the grid topology changes, requiring stencils to be modified. Combining these building blocks results in a finite-volume discretization for conservation laws on 3D cubed-sphere grids that is uniformly high-order accurate in all three grid directions. While solution-adaptivity is natural in the multi-block setting of our code, high-order accurate adaptive refinement on cubed-sphere grids is not pursued in this paper. The 3D CENO scheme is an accurate and robust solution method for hyperbolic conservation laws on general hexahedral grids that is attractive because it is inherently multidimensional by employing a K-exact overdetermined reconstruction scheme, and it avoids the complexity of considering multiple non-central stencil configurations that characterizes traditional ENO schemes. Extensive numerical tests demonstrate fourth-order convergence for stationary and time-dependent Euler and magnetohydrodynamic flows on cubed-sphere grids, and robustness against spurious oscillations at 3D shocks. Performance tests illustrate efficiency gains that can be potentially achieved using fourth-order schemes as compared to second-order methods for the same error level. Applications on extended cubed-sphere grids incorporating a seventh root block that discretizes the interior of the inner sphere demonstrate the versatility of the spatial discretization method.

A mimetic, semi-implicit, forward-in-time, finite volume shallow water model: comparison of hexagonal–icosahedral and cubed-sphere grids

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.

Reprint of: A conservative multi-tracer transport scheme for spectral-element spherical grids

Atmospheric models used for practical climate simulation must be capable handling the transport of hundreds of tracers. For computational efficiency conservative multi-tracer semi-Lagrangian type transport schemes are appropriate. Global models based on high-order Galerkin approach employ highly non-uniform spectral-element grids, and semi-Lagrangian transport is a challenge on those grids. A conservative semi-Lagrangian scheme (SPELT — SPectral-Element Lagrangian Transport) employing a multi-moment compact reconstruction procedure is developed for non-uniform quadrilateral grids. The scheme is based on a characteristic semi-Lagrangian method that avoids complex and expensive upstream area computations. The SPELT scheme has been implemented in the High-Order Method Modeling Environment (HOMME), which is based on a cubed-sphere grid with spectral-element spatial discretization. Additionally, we show the (strong) scalability and multi-tracer efficiency using several benchmark tests. The SPELT solution can be made monotonic (positivity preserving) by combining the flux-corrected transport algorithm, which is demonstrated on a uniform resolution grid. In particular, SPELT can be efficiently used for non-uniform grids and provides accurate and stable results for high-resolution meshes.

Intercomparison of general circulation models for hot extrasolar planets

We compare five general circulation models (GCMs) which have been recently used to study hot extrasolar planet atmospheres (BOB, CAM, IGCM, MITgcm, and PEQMOD), under three test cases useful for assessing model convergence and accuracy. Such a broad, detailed intercomparison has not been performed thus far for extrasolar planets study. The models considered all solve the traditional primitive equations, but employ different numerical algorithms or grids (e.g., pseudospectral and finite volume, with the latter separately in longitude–latitude and ‘cubed-sphere’ grids). The test cases are chosen to cleanly address specific aspects of the behaviors typically reported in hot extrasolar planet simulations: (1) steady-state, (2) nonlinearly evolving baroclinic wave, and (3) response to fast timescale thermal relaxation. When initialized with a steady jet, all models maintain the steadiness, as they should—except MITgcm in cubed-sphere grid. A very good agreement is obtained for a baroclinic wave evolving from an initial instability in pseudospectral models (only). However, exact numerical convergence is still not achieved across the pseudospectral models: amplitudes and phases are observably different. When subject to a typical ‘hot-Jupiter’-like forcing, all five models show quantitatively different behavior—although qualitatively similar, time-variable, quadrupole-dominated flows are produced. Hence, as have been advocated in several past studies, specific quantitative predictions (such as the location of large vortices and hot regions) by GCMs should be viewed with caution. Overall, in the tests considered here, pseudospectral models in pressure coordinate (PEBOB and PEQMOD) perform the best and MITgcm in cubed-sphere grid performs the worst.

Global shallow water models based on multi-moment constrained finite volume method and three quasi-uniform spherical grids

This is a review article to present several accurate and computationally efficient global models for shallow water equations recently developed under a general numerical framework, the multi-moment constrained finite volume (MCV) method. The multi-moment constrained finite volume method defines the unknowns (prognostic variables) as the point values at the solution points located over each mesh element. The time evolution equations to update these unknowns are derived through the constraint conditions on different moments, e.g. the point value (PV) and the volume-integrated average (VIA). Rigorous numerical conservation is guaranteed by the constraint on the VIA moment through a finite volume formulation of flux form. The resulted numerical schemes are very simple, efficient and easy to implement for both structured and unstructured grids. We have implemented the MCV method to three major spherical grids, Yin–Yang overset grid, cubed-sphere grid and geodesic icosahedral grid, which have overall quasi-uniform grid spacings and are highly popular in the community of global modeling for atmospheric and oceanic dynamics. In this paper, we present the global shallow water models based on these three spherical grids and the third-order MCV scheme. We evaluate and compare the models by widely used benchmark tests, which show the third-order convergence rate for all models, and the numerical results are competitive to other exiting models. Using MCV method as a numerical formulation is well-balanced between solution quality and computational simplicity, the proposed models provide accurate and practical bases for developing dynamic core of general circulation models on different spherical grids.

A conservative multi-tracer transport scheme for spectral-element spherical grids

Atmospheric models used for practical climate simulation must be capable handling the transport of hundreds of tracers. For computational efficiency conservative multi-tracer semi-Lagrangian type transport schemes are appropriate. Global models based on high-order Galerkin approach employ highly non-uniform spectral-element grids, and semi-Lagrangian transport is a challenge on those grids. A conservative semi-Lagrangian scheme (SPELT — SPectral-Element Lagrangian Transport) employing a multi-moment compact reconstruction procedure is developed for non-uniform quadrilateral grids. The scheme is based on a characteristic semi-Lagrangian method that avoids complex and expensive upstream area computations. The SPELT scheme has been implemented in the High-Order Method Modeling Environment (HOMME), which is based on a cubed-sphere grid with spectral-element spatial discretization. Additionally, we show the (strong) scalability and multi-tracer efficiency using several benchmark tests. The SPELT solution can be made monotonic (positivity preserving) by combining the flux-corrected transport algorithm, which is demonstrated on a uniform resolution grid. In particular, SPELT can be efficiently used for non-uniform grids and provides accurate and stable results for high-resolution meshes.

Multi-dimensional finite-volume scheme for hyperbolic conservation laws on three-dimensional solution-adaptive cubed-sphere grids

A scalable parallel and block-adaptive cubed-sphere grid simulation framework is described for solution of hyperbolic conservation laws in domains between two concentric spheres. In particular, the Euler and ideal magnetohydrodynamics (MHD) equations are considered. Compared to existing cubed-sphere grid algorithms, a novelty of the proposed approach involves the use of a fully multi-dimensional finite-volume method. This leads to important advantages when the treatment of boundaries and corners of the six sectors of the cubed-sphere grid is considered. Most existing finite-volume approaches use dimension-by-dimension differencing and require special interpolation or reconstruction procedures at ghost cells adjacent to sector boundaries in order to achieve an order of solution accuracy higher than unity. In contrast, in our multi-dimensional approach, solution blocks adjacent to sector boundaries can directly use physical cells from the adjacent sector as ghost cells while maintaining uniform second-order accuracy. This leads to important advantages in terms of simplicity of implementation for both parallelism and adaptivity at sector boundaries. Crucial elements of the proposed scheme are: unstructured connectivity of the six grid root blocks that correspond to the six sectors of the cubed-sphere grid, multi-dimensional k-exact reconstruction that automatically takes into account information from neighbouring cells isotropically and is able to automatically handle varying stencil size, and adaptive division of the solution blocks into smaller blocks of varying spatial resolution that are all treated exactly equally for inter-block communication, flux calculation, adaptivity and parallelization. The proposed approach is fully three-dimensional, whereas previous studies on cubed-sphere grids have been either restricted to two-dimensional geometries on the sphere or have grids and solution methods with limited capabilities in the third dimension in terms of adaptivity and parallelism. Numerical results for several problems, including systematic grid convergence studies, MHD bow-shock flows, and global modelling of solar wind flow are discussed to demonstrate the accuracy and efficiency of the proposed solution procedure, along with assessment of parallel computing scalability for up to thousands of computing cores.

On Mass Conservation in High-Order High-Resolution Rigorous Remapping Schemes on the Sphere

AbstractIt is the purpose of this short article to analyze mass conservation in high-order rigorous remapping schemes, which contrary to flux-based methods, relies on elaborate integral constraints over overlap areas and reconstruction functions. For applications on the sphere these integral constraints may be violated primarily as a result of inexact or ill-conditioned integration and the authors propose a generic, local, and multitracer efficient method that guarantees that the integral constraints are satisfied in discrete space irrespective of the accuracy of the numerical integration method and slight inaccuracies in the computation of overlap areas. The authors refer to this method as enforcement of consistency as it is based on integral constraints valid in continuous space. The consistency enforcement method is illustrated in idealized transport tests with the Conservative Semi-Lagrangian Multitracer scheme (CSLAM) in the High Order Method Modeling Environment (HOMME) where the analytic integrals, which were found to be ill conditioned at certain resolutions and flow conditions, have been replaced with robust quadrature. This violates mass conservation; however, with the consistency enforcement method, mass conservation is inherent even with low-order quadrature and renders rigorous remap schemes such as CSLAM (which was previously limited to gnomonic cubed-sphere grids) mass conservative on any spherical grid.

Hermitian Compact Interpolation on the Cubed-Sphere Grid

The cubed-sphere grid is a spherical grid made of six quasi-cartesian square-like patches. It was originally introduced in Sadourny (Mon Weather Rev 100:136---144, 1972). We extend to this grid the design of high-order finite-difference compact operators (Collatz, The numerical treatment of differential equations. Springer, Berlin, 1960; Lele, J Comput Phys 103:16---42, 1992). The present work is limitated to the design of a fourth-order accurate spherical gradient. The treatment at the interface of the six patches relies on a specific interpolation system which is based on using great circles in an essential way. The main interest of the approach is a fully symmetric treatment of the sphere. We numerically demonstrate the accuracy of the approximate gradient on several test problems, including the cosine-bell test-case of Williamson et al. (J Comput Phys 102:211---224, 1992) and a deformational test-case reported in Nair and Lauritzen (J Comput Phys 229:8868---8887, 2010).

AMIP Simulation with the CAM4 Spectral Element Dynamical Core

Abstract The authors evaluate the climate produced by the Community Climate System Model, version 4, running with the new spectral element atmospheric dynamical core option. The spectral element method is configured to use a cubed-sphere grid, providing quasi-uniform resolution over the sphere and increased parallel scalability and removing the need for polar filters. It uses a fourth-order accurate spatial discretization that locally conserves mass and total energy. Using the Atmosphere Model Intercomparison Project protocol, the results from the spectral element dynamical core are compared with those produced by the default finite-volume dynamical core and with observations. Even though the two dynamical cores are quite different, their simulated climates are remarkably similar. When compared with observations, both models have strengths and weaknesses but have nearly identical root-mean-square errors and the largest biases show little sensitivity to the dynamical core. The spectral element core does an excellent job reproducing the atmospheric kinetic energy spectra, including fully capturing the observed Nastrom–Gage transition when running at 0.125° resolution.

A Two-Way Nested Global-Regional Dynamical Core on the Cubed-Sphere Grid

Abstract A nested-grid model is constructed using the Geophysical Fluid Dynamics Laboratory finite-volume dynamical core on the cubed sphere. The use of a global grid avoids the need for externally imposed lateral boundary conditions, and the use of the same governing equations and discretization on the global and regional domains prevents inconsistencies that may arise when these differ between grids. A simple interpolated nested-grid boundary condition is used, and two-way updates use a finite-volume averaging method. Mass conservation is achieved in two-way nesting by simply not updating the mass field. Despite the simplicity of the nesting methodology, the distortion of the large-scale flow by the nested grid is such that the increase in global error norms is a factor of 2 or less in shallow-water test cases. The effect of a nested grid in the tropics on the zonal means and eddy statistics of an idealized Held–Suarez climate integration is minor, and artifacts due to the nested grid are comparable to those at the edges of the cubed-sphere grid and decrease with increasing resolution. The baroclinic wave train in a Jablonowski–Williamson test case was preserved in a nested-grid simulation while finescale features were represented with greater detail in the nested-grid region. The authors also found that lee vortices could propagate out of the nested region and onto a coarse grid, which by itself could not produce vortices. Finally, the authors discuss how concurrent integration of the nested and coarse grids can be significantly more efficient than when integrating the two grids sequentially.

Integrating a scalable and effcient semi-Lagrangian multi-tracer transport scheme in HOMME

With the inclusion of a scalable spectral-element-based version of the High-Order Method Modeling Environment (HOMME) in NCAR's Community Atmosphere Model (CAM) and the need for on the order of 100 prognostic tracers in next generation climate modeling efforts, there is an urgent need for a scalable, monotonic, and conservative multitracer advection scheme in HOMME. To address this, we integrate a Conservative Semi-LAgrangian Multi-tracer transport scheme (CSLAM) into HOMME. The algorithm is specifically re-designed for multiple processors and the cubed-sphere grid with the element-wise domain decomposition as employed by HOMME. Based on these spectral elements, we create a finite volume mesh and add a halo zone of cells since a higher-order CSLAM needs a patch of tracer values for a reconstruction that extend the element. Therefore, we extend HOMME to also be capable of communicating cell center data. Our data structures and design allow us to provide a numerical scheme that still conserves mass locally to machine precision and is also monotone on multiple processor systems, but reduces the communication of tracer values by one for each time step. This is based on the idea that we calculate the reconstruction coeffcients redundantly, in a cell of an element and in the corresponding cell in the halo zone. Our algorithm of CSLAM in HOMME is the first one for multiple processor systems and multi-tracers that is highly scalable and effcient.

CAM-SE: A scalable spectral element dynamical core for the Community Atmosphere Model

The Community Atmosphere Model (CAM) version 5 includes a spectral element dynamical core option from NCAR’s High-Order Method Modeling Environment. It is a continuous Galerkin spectral finite-element method designed for fully unstructured quadrilateral meshes. The current configurations in CAM are based on the cubed-sphere grid. The main motivation for including a spectral element dynamical core is to improve the scalability of CAM by allowing quasi-uniform grids for the sphere that do not require polar filters. In addition, the approach provides other state-of-the-art capabilities such as improved conservation properties. Spectral elements are used for the horizontal discretization, while most other aspects of the dynamical core are a hybrid of well-tested techniques from CAM’s finite volume and global spectral dynamical core options. Here we first give an overview of the spectral element dynamical core as used in CAM. We then give scalability and performance results from CAM running with three different dynamical core options within the Community Earth System Model, using a pre-industrial time-slice configuration. We focus on high-resolution simulations, using 1/4 degree, 1/8 degree, and T341 spectral truncation horizontal grids.

Evaluation of the HOMME Dynamical Core in the Aquaplanet Configuration of NCAR CAM4: Rainfall

Abstract The NCAR Community Climate System Model, version 4 (CCSM4), includes a new dynamical core option based on NCAR’s High-Order Method Modeling Environment (HOMME). HOMME is a petascale-capable high-order element-based conservative dynamical core developed on the cubed-sphere grid. Initial simulations have been completed in an aquaplanet configuration of the Community Atmosphere Model, version 4 (CAM4), the atmospheric component of CCSM4. The authors examined the results of this simulation and assessed its fidelity in simulating rainfall, which is one of the most important components of the earth’s climate system. For this they compared the results from two other dynamical cores of CAM4: the finite volume (FV) and Eulerian (EUL). Instantaneous features of rainfall in HOMME are similar to FV and EUL. Similar to EUL and FV, HOMME simulates a single-peak intertropical convergence zone (ITCZ) over the equator. The strength of the ITCZ is found to be almost the same in HOMME and EUL but more in FV. It is observed that in HOMME and EUL, there is higher surface evaporation, which supplies more moisture to the deep tropics and gives more rainfall over the ITCZ. The altitude of maximum precipitation is found to be at almost the same level in all three dynamical cores. The eastward propagation of rainfall bands is organized and more prominent in FV and HOMME than in EUL. The phase speed of the eastward propagation in HOMME is found to be higher than in FV. The results show that, in general, the rainfall simulated by HOMME falls in a regime between that of FV and EUL. Hence, they conclude that the key aspects of rainfall simulation with HOMME falls into an acceptable range, as compared to the existing dynamical cores used in the model.

Performance of the HOMME dynamical core in the aqua-planet configuration of NCAR CAM4: equatorial waves

Abstract. A new atmospheric dynamical core, named the High Order Method Modeling Environment (HOMME), has been recently included in the NCAR-Community Climate System Model version 4 (CCSM4). It is a petascale capable high-order element-based conservative dynamical core developed on a cubed-sphere grid. We have examined the model simulations with HOMME using the aqua-planet mode of CAM4 (atmospheric component of CCSM4) and evaluated its performance in simulating the equatorial waves, considered a crucial element of climate variability. For this we compared the results with two other established models in CAM4 framework, which are the finite-volume (FV) and Eulerian spectral (EUL) dynamical cores. Although the gross features seem to be comparable, important differences have been found among the three dynamical cores. The phase speed of Kelvin waves in HOMME is faster and more satisfactory than those in FV and EUL. The higher phase speed is attributed to an increased large-scale precipitation in the upper troposphere and a more top-heavy heating structure. The variance of the n=1 equatorial Rossby waves is underestimated by all three of them, but comparatively HOMME simulations are more reasonable. For the n=0 eastward inertio-gravity waves, the variances are weak and phase speeds are too slow, scaled to shallow equivalent depths. However, the variance in HOMME is relatively more compared to the two other dynamical cores. The mixed Rossby-gravity waves are feeble in all the three cases. In summary, model simulations using HOMME are reasonably good, with some improvement relative to FV and EUL in capturing some of the important characteristics associated with equatorial waves.

An Adaptive Multimoment Global Model on a Cubed Sphere

Abstract An adaptive global shallow-water model is proposed on cubed-sphere grid using the multimoment finite volume scheme and the Berger–Oliger adaptive mesh refinement (AMR) algorithm that was originally designed for a Cartesian grid. On each patch of the cubed-sphere grid, the curvilinear coordinates are constructed in a way that the Berger–Oliger algorithm can be applied directly. Moreover, an algorithm to transfer data across neighboring patches is proposed to establish a practical integrated framework for global AMR computation on the cubed-sphere grid. The multimoment finite volume scheme is adopted as the fluid solver and is essentially beneficial to the implementation of AMR on the cubed-sphere grid. The multimoment interpolation based on both volume-integrated average (VIA) and point value (PV) provides the compact reconstruction that makes the present scheme very attractive not only in dealing with the artificial boundaries between different patches but also in the coarse–fine interpolations required in the AMR computations. The single-cell-based reconstruction avoids involving more than two nesting levels during interpolations. The reconstruction profile of constrained interpolation profile–conservative semi-Lagrangian scheme with third-order polynomial function (CIP-CSL3) is adopted where the slope parameter provides a flexible and convenient switching to get the desired numerical properties, such as high-order (fourth order) accuracy, monotonicity, and positive definiteness. Numerical experiments with typical benchmark tests for both advection equation and shallow-water equations are carried out to evaluate the proposed model. The numerical errors and the corresponding CPU times of numerical experiments on uniform and adaptive meshes verify the performance of the proposed model. Compared to the uniformly refined grid, the AMR technique is able to achieve the similar numerical accuracy with less computational cost.

A multi-moment transport model on cubed-sphere grid

A conservative, single-cell-based semi-Lagrangian transport model is proposed in this paper. Using multi-moment concept, an additional moment, i.e. volume-integrated average (VIA), is treated as the model variable besides the point value (PV) updated in the traditional semi-Lagrangian schemes. A quadratic interpolation function is constructed based on local degrees of freedom defined within each single cell. The PV moment is advanced by the semi-Lagrangian formulation, whereas the VIA moment is updated by a finite volume formulation to rigorously ensure the numerical conservation. The numerical fluxes are computed from the PV moments defined along the boundary edges of the control volume. The scheme is extended to the spherical geometry through the application of the cubed-sphere grid that eliminates the polar singularity in the conventional longitude/latitude coordinates by using the quasi-uniform grid spacing covering the whole sphere. The single-cell-based scheme is well suited for the treatment of the connections between different patches. A simple quasi-monotone limiter to the PV moment is applied to suppress non-physical oscillations. The proposed scheme has been validated via representative benchmark tests and the performance is competitive to other existing transport schemes.